A New Methodology for the Development of Efficient Multistep Methods for First-Order IVPs with Oscillating Solutions
In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show how it can be applied to the Adams–Bashforth appro...
Gespeichert in:
| Veröffentlicht in: | Mathematics (Basel) Jg. 12; H. 4; S. 504 |
|---|---|
| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel
MDPI AG
01.02.2024
|
| Schlagworte: | |
| ISSN: | 2227-7390, 2227-7390 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show how it can be applied to the Adams–Bashforth approach in three steps. The stability of the new scheme is also analyzed. We compared the performance of our novel algorithm to that of established approaches and found it to be superior. Numerical experiments confirmed that, in comparison to standard approaches to the numerical solution of Initial Value Problems (IVPs), including oscillating solutions, our approach is significantly more effective. |
|---|---|
| AbstractList | In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show how it can be applied to the Adams–Bashforth approach in three steps. The stability of the new scheme is also analyzed. We compared the performance of our novel algorithm to that of established approaches and found it to be superior. Numerical experiments confirmed that, in comparison to standard approaches to the numerical solution of Initial Value Problems (IVPs), including oscillating solutions, our approach is significantly more effective. |
| Audience | Academic |
| Author | Simos, Theodore |
| Author_xml | – sequence: 1 givenname: Theodore orcidid: 0000-0002-9220-6924 surname: Simos fullname: Simos, Theodore |
| BookMark | eNptkU1vGyEQhlGVSk3d3PoDkHrtpsCyy3K00qSxlMSV-nFFLDtjY60XF3Cj_PvgOJWiKsxhmGGeV8D7npxMYQJCPnJ2XteafdnavOaCSdYw-YacCiFUpcrByYv9O3KW0oaVpXndSX1K8pzewT29hbwOQxjD6oFiiDSvgX6FvzCG3RamTAPSS0Tv_KG43Y_Zpwy7Zyw9IVc-plwt4wCRLn5_T_Te5zVdJufH0WY_reiPMO6zD1P6QN6iHROcPecZ-XV1-fPiurpZfltczG8qJ1mbKysVcw1rwQH2HPsOrVV8cEy3tukbjgO2rO85YFc7jcgH6UB0QmPj-q629YwsjrpDsBuzi35r44MJ1punRogrY2P2bgRT986haFSHHUg76B7QykGqxinWCA1F69NRaxfDnz2kbDZhH6dyfSN0zbTSuuQZOT9OrWwR9ROGHK0rMcDWu2IY-tKfq05yJrhqCyCOgIshpQhonM_28EsF9KPhzBzcNS_dLdDn_6B_b3t1_BHxd6pQ |
| CitedBy_id | crossref_primary_10_3390_axioms13080514 crossref_primary_10_1007_s40314_025_03203_0 crossref_primary_10_3390_math13111833 crossref_primary_10_1016_j_apnum_2024_08_024 crossref_primary_10_3390_math12233652 crossref_primary_10_1007_s10910_025_01727_8 crossref_primary_10_3390_math12233824 crossref_primary_10_1016_j_mex_2024_103045 crossref_primary_10_3390_sym16050508 crossref_primary_10_1007_s00009_025_02876_5 crossref_primary_10_1007_s10910_025_01748_3 crossref_primary_10_1016_j_matcom_2025_05_024 crossref_primary_10_3390_axioms13090649 |
| Cites_doi | 10.1016/0377-0427(84)90002-5 10.1016/S0010-4655(02)00676-8 10.1016/j.apm.2012.05.001 10.1016/S0097-8485(00)00087-5 10.1016/j.cam.2007.05.016 10.1007/s10910-017-0762-8 10.1002/9780470141526 10.1016/j.cam.2011.07.004 10.1007/s10092-022-00456-7 10.1016/j.apnum.2005.09.005 10.1023/A:1016629706668 10.1137/S0036142995286763 10.1016/j.cpc.2007.07.007 10.1007/s11075-008-9202-y 10.1515/math-2021-0009 10.1016/j.physrep.2009.07.005 10.1016/j.cam.2008.11.011 10.1007/s10543-010-0250-z 10.1016/j.apnum.2008.04.002 10.1016/0010-4655(78)90047-4 10.1016/j.newast.2004.12.004 10.1016/S0377-0427(96)00165-3 10.1142/S0129183198000200 10.1016/S0377-0427(97)00188-X 10.1016/S0377-0427(99)00340-4 10.1016/0010-4655(85)90100-6 10.1016/j.apnum.2004.01.005 10.1007/s40096-021-00420-6 10.1016/0377-0427(86)90094-4 10.1007/BF01937488 10.1016/j.cpc.2004.11.002 10.1007/s40314-021-01728-8 10.1142/S0129183101002826 10.1016/0898-1221(95)00155-R 10.1016/j.cam.2006.10.025 10.1016/j.cam.2008.01.026 10.1007/s10910-009-9626-1 10.1016/S0377-0427(96)00156-2 10.1007/s11075-007-9142-y 10.1155/2011/407151 10.1016/j.cpc.2005.09.005 10.1016/S0377-0427(99)00055-2 10.1016/S0010-4655(02)00460-5 10.1016/0377-0427(86)90224-4 10.1016/j.cpc.2010.08.019 10.1016/j.cpc.2009.04.005 10.1016/S0377-0427(00)00599-9 10.1007/s41980-023-00765-9 10.1145/79505.79507 10.1016/j.cpc.2006.07.015 10.1007/BF02163234 10.1002/mma.8528 10.1016/0377-0427(90)90001-G 10.1016/0898-1221(95)00196-4 10.1016/j.cam.2004.05.017 10.1016/0771-050X(80)90013-3 10.1016/0010-4655(83)90036-X 10.1016/0021-9991(87)90139-2 10.1142/S0129183106009394 10.1016/j.cam.2005.01.020 10.1086/115629 10.1080/00207160.2018.1437263 10.1016/j.cpc.2006.03.004 10.1016/j.cam.2003.12.015 10.1016/j.cpc.2012.06.013 10.1016/j.cam.2020.113312 10.1016/0010-4655(87)90020-8 10.1016/j.camwa.2006.06.012 10.1007/BF01952791 10.1016/j.cpc.2012.12.018 10.1007/s13370-023-01075-3 10.1016/j.cam.2013.10.015 10.1016/j.cam.2004.03.003 10.1007/s10910-009-9606-5 10.1016/j.cam.2005.04.028 10.1016/0377-0427(96)00005-2 10.1016/j.cpc.2008.01.046 10.1142/S0129183107010449 10.1016/j.aml.2010.07.003 10.1016/0010-4655(80)90062-4 10.1002/qua.560530504 10.1016/j.aej.2023.04.026 10.1007/BF01395931 10.1016/0010-4655(87)90013-0 10.3390/math9030232 10.1137/0718030 10.1016/j.cpc.2007.05.003 10.1016/j.mcm.2005.09.015 10.1093/imanum/9.2.145 10.1016/j.apnum.2006.12.003 10.47836/pjst.31.2.10 10.1016/0377-0427(87)90113-0 10.1137/050641752 10.1007/s12190-021-01575-0 10.1093/imanum/16.2.179 10.1016/S0377-0427(01)00474-5 10.1016/0010-4655(81)90101-6 10.1016/j.cam.2003.03.002 10.1080/00207169808804642 10.1016/j.cpc.2014.05.030 10.1007/s10910-011-9824-5 10.47836/mjms.16.4.07 10.3390/math9080806 10.3390/math7121197 10.1007/BF02281728 10.1016/j.physrep.2013.11.003 10.1016/S0010-4655(96)00147-6 10.1093/imanum/7.2.235 10.1016/j.apnum.2008.03.018 |
| ContentType | Journal Article |
| Copyright | COPYRIGHT 2024 MDPI AG 2024 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: COPYRIGHT 2024 MDPI AG – notice: 2024 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | AAYXX CITATION 3V. 7SC 7TB 7XB 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ HCIFZ JQ2 K7- KR7 L6V L7M L~C L~D M0N M7S P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PTHSS Q9U DOA |
| DOI | 10.3390/math12040504 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials - QC ProQuest Central Technology Collection ProQuest One ProQuest Central Korea Engineering Research Database ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database (ProQuest) Civil Engineering Abstracts ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Engineering Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition Engineering Collection ProQuest Central Basic DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef Publicly Available Content Database Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts ProQuest Computing Engineering Database ProQuest Central Basic ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) |
| DatabaseTitleList | CrossRef Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: PIMPY name: ProQuest - Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2227-7390 |
| ExternalDocumentID | oai_doaj_org_article_3bccf2578f8e4ad9befa4d475c70529e A784102176 10_3390_math12040504 |
| GroupedDBID | -~X 5VS 85S 8FE 8FG AADQD AAFWJ AAYXX ABDBF ABJCF ABPPZ ABUWG ACIPV ACIWK ADBBV AFFHD AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS AMVHM ARAPS AZQEC BCNDV BENPR BGLVJ BPHCQ CCPQU CITATION DWQXO GNUQQ GROUPED_DOAJ HCIFZ IAO ITC K6V K7- KQ8 L6V M7S MODMG M~E OK1 PHGZM PHGZT PIMPY PQGLB PQQKQ PROAC PTHSS RNS 3V. 7SC 7TB 7XB 8AL 8FD 8FK FR3 JQ2 KR7 L7M L~C L~D M0N P62 PKEHL PQEST PQUKI Q9U |
| ID | FETCH-LOGICAL-c406t-a470c506ecefb1fb8faa71dc096a5b51fdf60bb1ef83c9ff1d4ce2829f5cb83a3 |
| IEDL.DBID | DOA |
| ISICitedReferencesCount | 15 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001169804000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2227-7390 |
| IngestDate | Fri Oct 03 12:38:40 EDT 2025 Fri Jul 25 12:10:27 EDT 2025 Tue Nov 04 18:33:44 EST 2025 Sat Nov 29 07:13:24 EST 2025 Tue Nov 18 22:41:41 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c406t-a470c506ecefb1fb8faa71dc096a5b51fdf60bb1ef83c9ff1d4ce2829f5cb83a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-9220-6924 |
| OpenAccessLink | https://doaj.org/article/3bccf2578f8e4ad9befa4d475c70529e |
| PQID | 2930979929 |
| PQPubID | 2032364 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_3bccf2578f8e4ad9befa4d475c70529e proquest_journals_2930979929 gale_infotracacademiconefile_A784102176 crossref_citationtrail_10_3390_math12040504 crossref_primary_10_3390_math12040504 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-02-01 |
| PublicationDateYYYYMMDD | 2024-02-01 |
| PublicationDate_xml | – month: 02 year: 2024 text: 2024-02-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Basel |
| PublicationPlace_xml | – name: Basel |
| PublicationTitle | Mathematics (Basel) |
| PublicationYear | 2024 |
| Publisher | MDPI AG |
| Publisher_xml | – name: MDPI AG |
| References | Konguetsof (ref_100) 2010; 47 Konguetsof (ref_92) 2017; 55 ref_131 Demba (ref_43) 2023; 21 ref_132 Avdelas (ref_9) 2000; 62 Ixaru (ref_79) 2001; 132 (ref_97) 2007; 209 Konguetsof (ref_93) 2011; 49 ref_18 Chawla (ref_63) 1987; 17 Fang (ref_96) 2007; 189 (ref_95) 2007; 53 Ferrandiz (ref_6) 1998; 35 Raptis (ref_82) 1982; 28 Simos (ref_127) 2013; 37 Franco (ref_29) 2009; 59 Shokri (ref_113) 2020; 376 Franco (ref_126) 1990; 30 Franco (ref_91) 2014; 232 Stiefel (ref_122) 1969; 13 Quinlan (ref_10) 1990; 100 ref_121 Franco (ref_34) 2006; 56 ref_123 (ref_85) 2007; 46 (ref_94) 2006; 17 Chawla (ref_59) 1984; 11 Raptis (ref_112) 1991; 31 Ahmad (ref_45) 2020; 14 Wang (ref_110) 2007; 18 Daele (ref_103) 1995; 30 Avdelas (ref_11) 1996; 31 Raptis (ref_80) 1987; 44 Ixaru (ref_130) 2002; 140 Ixaru (ref_76) 1980; 19 Thomas (ref_5) 1997; 87 Calvo (ref_28) 2010; 50 Anastassi (ref_58) 2009; 482–483 Coleman (ref_108) 2006; 44 Calvo (ref_26) 2012; 236 Vyver (ref_21) 2005; 10 Lee (ref_46) 2023; 72 Wang (ref_111) 2006; 175 Ramos (ref_129) 2010; 23 Lyche (ref_14) 1972; 10 Franco (ref_24) 2014; 260 Wang (ref_104) 2006; 174 Avdelas (ref_12) 1996; 72 Franco (ref_56) 2003; 161 Ixaru (ref_68) 1987; 73 Vyver (ref_22) 2006; 188 (ref_40) 2005; 184 Ramos (ref_41) 2008; 178 Dormand (ref_54) 1980; 6 Chawla (ref_62) 1986; 16 Franco (ref_125) 2001; 26 Franco (ref_55) 2004; 50 Konguetsof (ref_17) 2001; 1 Coleman (ref_64) 1989; 9 Simos (ref_13) 1995; 53 (ref_98) 2008; 60 Chen (ref_49) 2022; 59 Tocino (ref_38) 2005; 42 Cash (ref_124) 1990; 16 Calvo (ref_27) 2010; 181 Chien (ref_47) 2023; 31 Paternoster (ref_109) 2012; 183 Franco (ref_36) 2005; 173 Ixaru (ref_67) 1987; 44 Wang (ref_105) 2006; 175 (ref_39) 2005; 166 Fang (ref_86) 2008; 58 Dormand (ref_20) 1987; 7 Fang (ref_53) 2020; 97 Franco (ref_25) 2013; 184 Godwin (ref_116) 2022; 28 Calvo (ref_30) 2009; 223 Franco (ref_33) 2007; 177 Ixaru (ref_70) 1997; 79 Senu (ref_50) 2022; 41 Franco (ref_89) 2016; 273 Rizea (ref_78) 2010; 48 Salih (ref_115) 2022; 16 Simos (ref_60) 1997; 79 Coleman (ref_66) 2000; 126 Lee (ref_117) 2022; 16 Fatheah (ref_101) 2011; 2011 Thomas (ref_61) 1984; 24 Raptis (ref_81) 1983; 28 Senu (ref_52) 2021; 15 Fang (ref_120) 2021; 392 Chawla (ref_77) 1986; 15 Franco (ref_23) 2015; 252 Tang (ref_107) 2005; 173 Raptis (ref_15) 1978; 14 Ixaru (ref_69) 1997; 100 Tang (ref_106) 2004; 169 ref_119 Ixaru (ref_73) 2001; 25 Calvo (ref_31) 2008; 218 Kalogiratou (ref_57) 2014; 536 Franco (ref_35) 2002; 147 Wu (ref_37) 2009; 180 (ref_99) 2008; 48 Wang (ref_102) 2005; 461 Simos (ref_19) 2001; 10 Petzold (ref_128) 1981; 18 Hollevoet (ref_88) 2009; 230 Daele (ref_71) 1998; 66 Ixaru (ref_74) 2003; 150 Ixaru (ref_72) 1999; 106 Berghe (ref_87) 2009; 59 Coleman (ref_65) 1996; 16 Raptis (ref_4) 1984; 25 Ixaru (ref_75) 1985; 38 ref_44 Demba (ref_42) 2023; 49 Raptis (ref_83) 1981; 24 Demba (ref_48) 2023; 46 ref_1 ref_3 ref_2 Obaidat (ref_118) 2021; 19 Raptis (ref_84) 1980; 24 ref_8 Zhai (ref_51) 2022; 68 Abdulganiy (ref_114) 2023; 34 Simos (ref_16) 1998; 9 Franco (ref_90) 2014; 185 ref_7 Calvo (ref_32) 2008; 178 |
| References_xml | – volume: 11 start-page: 277 year: 1984 ident: ref_59 article-title: A Noumerov-Type Method with Minimal Phase-Lag for the Integration of 2nd Order Periodic Initial-Value Problems publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(84)90002-5 – volume: 150 start-page: 116 year: 2003 ident: ref_74 article-title: Exponentially Fitted Variable Two-Step BDF Algorithm for First Order Odes publication-title: Comput. Phys. Commun. doi: 10.1016/S0010-4655(02)00676-8 – volume: 14 start-page: 403 year: 2020 ident: ref_45 article-title: Higher Order Three Derivative Runge–Kutta Method with Phase–Fitting and Amplification–Fitting Technique for Periodic IVPs publication-title: Malays. J. Math. Sci. – volume: 37 start-page: 1983 year: 2013 ident: ref_127 article-title: New Open Modified Newton Cotes Type Formulae as Multilayer Symplectic Integrators publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2012.05.001 – volume: 25 start-page: 39 year: 2001 ident: ref_73 article-title: Numerical operations on oscillatory functions publication-title: Comput. Chem. doi: 10.1016/S0097-8485(00)00087-5 – volume: 218 start-page: 421 year: 2008 ident: ref_31 article-title: Structure preservation of exponentially fitted Runge-Kutta Methods publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.05.016 – volume: 28 start-page: 73 year: 2022 ident: ref_116 article-title: An efficient block solver of trigonometrically fitted method for stiff odes publication-title: Adv. Differ. Equ. Control Process. – volume: 55 start-page: 1808 year: 2017 ident: ref_92 article-title: A generator of families of two-Step numerical Methods with free parameters and minimal phase-lag publication-title: J. Math. Chem. doi: 10.1007/s10910-017-0762-8 – ident: ref_2 doi: 10.1002/9780470141526 – volume: 236 start-page: 3665 year: 2012 ident: ref_26 article-title: On some new low storage implementations of time advancing Runge-Kutta Methods publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2011.07.004 – volume: 59 start-page: 14 year: 2022 ident: ref_49 article-title: Optimal three-stage implicit exponentially-fitted RKN methods for solving second-order ODEs publication-title: Calcolo doi: 10.1007/s10092-022-00456-7 – ident: ref_132 – volume: 62 start-page: 1375 year: 2000 ident: ref_9 article-title: Dissipative high phase-lag order Numerov-type methods for the numerical solution of the Schrödinger equation publication-title: Phys. Rev. – volume: 56 start-page: 1040 year: 2006 ident: ref_34 article-title: New Methods for oscillatory systems based on ARKN Methods publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2005.09.005 – ident: ref_1 – volume: 26 start-page: 347 year: 2001 ident: ref_125 article-title: Four-stage symplectic and P–stable SDIRKN methods with dispersion of high order publication-title: Numer. Algorithms doi: 10.1023/A:1016629706668 – ident: ref_123 – volume: 35 start-page: 1684 year: 1998 ident: ref_6 article-title: A general procedure for the adaptation of multistep algorithms to the integration of oscillatory problems publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142995286763 – volume: 252 start-page: 45 year: 2015 ident: ref_23 article-title: Two new embedded pairs of explicit Runge-Kutta Methods adapted to the numerical solution of oscillatory problems publication-title: Appl. Math. Comput. – volume: 178 start-page: 15 year: 2008 ident: ref_41 article-title: Exponential fitting BDF-Runge-Kutta Algorithms publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2007.07.007 – volume: 48 start-page: 327 year: 2008 ident: ref_99 article-title: Exponential fitted Gauss, Radau and Lobatto Methods of low order publication-title: Numer. Algorithms doi: 10.1007/s11075-008-9202-y – volume: 19 start-page: 225 year: 2021 ident: ref_118 article-title: A new implicit symmetric method of sixth algebraic order with vanished phase-lag and its first derivative for solving Schrodinger’s equation publication-title: Open Math. doi: 10.1515/math-2021-0009 – volume: 482–483 start-page: 1 year: 2009 ident: ref_58 article-title: Numerical multistep methods for the efficient solution of quantum mechanics and related problems publication-title: Phys. Rep. doi: 10.1016/j.physrep.2009.07.005 – volume: 230 start-page: 260 year: 2009 ident: ref_88 article-title: The Optimal Exponentially-Fitted Numerov Method for Solving Two-Point Boundary Value Problems publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2008.11.011 – volume: 50 start-page: 3 year: 2010 ident: ref_28 article-title: On high order symmetric and symplectic trigonometrically fitted Runge-Kutta Methods with an even number of stages publication-title: BIT Numer. Math. doi: 10.1007/s10543-010-0250-z – volume: 59 start-page: 959 year: 2009 ident: ref_29 article-title: Accuracy and linear Stability of RKN Methods for solving second-order stiff problems publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2008.04.002 – volume: 14 start-page: 1 year: 1978 ident: ref_15 article-title: Exponential—fitting methods for the numerical solution of the Schrödinger equation publication-title: Comput. Phys. Commun. doi: 10.1016/0010-4655(78)90047-4 – volume: 10 start-page: 261 year: 2005 ident: ref_21 article-title: A Symplectic Exponentially Fitted Modified Runge-Kutta-Nyström Method for the Numerical Integration of Orbital Problems publication-title: New Astron. doi: 10.1016/j.newast.2004.12.004 – volume: 376 start-page: 125116 year: 2020 ident: ref_113 article-title: A new family of explicit linear two-step singularly P-stable Obrechkoff methods for the numerical solution of second-order IVPs publication-title: Appl. Math. Comput. – volume: 79 start-page: 87 year: 1997 ident: ref_70 article-title: Four Step Methods for Y′′ = F(X,Y) publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(96)00165-3 – volume: 9 start-page: 271 year: 1998 ident: ref_16 article-title: An eighth order exponentially-fitted method for the numerical solution of the Schrödinger equation publication-title: Int. J. Mod. Phys. doi: 10.1142/S0129183198000200 – volume: 87 start-page: 215 year: 1997 ident: ref_5 article-title: A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrodinger equation publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(97)00188-X – volume: 126 start-page: 47 year: 2000 ident: ref_66 article-title: Mixed Collocation Methods for Y′′ = F(X,Y) publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(99)00340-4 – volume: 38 start-page: 329 year: 1985 ident: ref_75 article-title: Comparison of some four-Step Methods for the numerical solution of the Schrödinger equation publication-title: Comput. Phys. Commun. doi: 10.1016/0010-4655(85)90100-6 – volume: 273 start-page: 493 year: 2016 ident: ref_89 article-title: Explicit exponentially fitted two-Step hybrid Methods of high order for second-order oscillatory IVPs publication-title: Appl. Math. Comput. – volume: 50 start-page: 427 year: 2004 ident: ref_55 article-title: Runge-Kutta methods adapted to the numerical integration of oscillatory problems publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2004.01.005 – volume: 28 start-page: 373 year: 1982 ident: ref_82 article-title: 2-Step Methods for the Numerical-Solution of the Schrödinger-Equation publication-title: Comput. Phys. Commun. – volume: 16 start-page: 281 year: 2022 ident: ref_117 article-title: High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge-Kutta-type methods for solving third-order oscillatory problems publication-title: Math. Sci. doi: 10.1007/s40096-021-00420-6 – ident: ref_3 – volume: 16 start-page: 233 year: 1986 ident: ref_62 article-title: 2-Step 4Th-Order P-Stable Methods with Phase-Lag of Order 6 for Y′′ = F(T,Y) publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(86)90094-4 – volume: 24 start-page: 225 year: 1984 ident: ref_61 article-title: Phase properties of high order, almost P-stable formulae publication-title: BIT Numer. Math. doi: 10.1007/BF01937488 – volume: 166 start-page: 109 year: 2005 ident: ref_39 article-title: Comparison of some special optimized fourth-order Runge-Kutta Methods for the numerical solution of the Schrödinger equation publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2004.11.002 – volume: 41 start-page: 25 year: 2022 ident: ref_50 article-title: Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation publication-title: Comput. Appl. Math. doi: 10.1007/s40314-021-01728-8 – volume: 10 start-page: 1453 year: 2001 ident: ref_19 article-title: On the construction of efficient methods for second order IVPs with oscillating solution publication-title: Int. J. Mod. Phys. doi: 10.1142/S0129183101002826 – volume: 30 start-page: 37 year: 1995 ident: ref_103 article-title: Properties and Implementation of R-Adams Methods Based On Mixed-Type Interpolation publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(95)00155-R – volume: 209 start-page: 33 year: 2007 ident: ref_97 article-title: Phase-fitted and amplification-fitted two-Step hybrid Methods for y′′ = f (x, y) publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2006.10.025 – volume: 223 start-page: 387 year: 2009 ident: ref_30 article-title: Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta Methods of the Gauss type publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2008.01.026 – volume: 60 start-page: 711 year: 2008 ident: ref_98 article-title: Efficient one-Step Methods for the Schrödinger equation publication-title: Match-Commun. Math. Comput. Chem. – volume: 48 start-page: 55 year: 2010 ident: ref_78 article-title: Exponential fitting Method for the time-dependent Schrödinger equation publication-title: J. Math. Chem. doi: 10.1007/s10910-009-9626-1 – volume: 79 start-page: 189 year: 1997 ident: ref_60 article-title: A Finite Difference Method for the numerical solution of the Schrödinger equation publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(96)00156-2 – volume: 46 start-page: 333 year: 2007 ident: ref_85 article-title: P-stable exponentially-fitted Obrechkoff Methods of arbitrary order for second-order differential equations publication-title: Numer. Algorithms doi: 10.1007/s11075-007-9142-y – volume: 2011 start-page: 407151 year: 2011 ident: ref_101 article-title: Hendi, P-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations publication-title: J. Appl. Math. doi: 10.1155/2011/407151 – volume: 174 start-page: 109 year: 2006 ident: ref_104 article-title: Trigonometrically-fitted Method with the Fourier frequency spectrum for undamped Duffing equation publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2005.09.005 – volume: 106 start-page: 87 year: 1999 ident: ref_72 article-title: A Conditionally P-Stable Fourth-Order Exponential-Fitting Method for Y′′ = F(X, Y) publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(99)00055-2 – volume: 147 start-page: 770 year: 2002 ident: ref_35 article-title: Runge-Kutta-Nyström Methods adapted to the numerical integration of perturbed oscillators publication-title: Comput. Phys. Commun. doi: 10.1016/S0010-4655(02)00460-5 – volume: 15 start-page: 329 year: 1986 ident: ref_77 article-title: A Noumerov-type Method with minimal phase-lag for the integration of second order periodic initial-value problems II Explicit Method publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(86)90224-4 – volume: 181 start-page: 2044 year: 2010 ident: ref_27 article-title: Symmetric and symplectic exponentially fitted Runge-Kutta Methods of high order publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2010.08.019 – volume: 180 start-page: 1545 year: 2009 ident: ref_37 article-title: Note on derivation of order conditions for ARKN Methods for perturbed oscillators publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2009.04.005 – volume: 132 start-page: 83 year: 2001 ident: ref_79 article-title: Weights of the Exponential Fitting Multistep Algorithms for First-Order Odes publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(00)00599-9 – volume: 49 start-page: 24 year: 2023 ident: ref_42 article-title: A Phase– and Amplification–Fitted 5(4) Diagonally Implicit Runge–Kutta–Nyström Pair for Oscillatory Systems publication-title: Bull. Iran. Math. Soc. doi: 10.1007/s41980-023-00765-9 – volume: 16 start-page: 201 year: 1990 ident: ref_124 article-title: A variable order Runge–Kutta method for initial value problems with rapidly varying right-hand sides publication-title: ACM Trans. Math. Softw. doi: 10.1145/79505.79507 – volume: 175 start-page: 692 year: 2006 ident: ref_111 article-title: Obrechkoff one-Step Method fitted with Fourier spectrum for undamped Duffing equation publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2006.07.015 – volume: 13 start-page: 154 year: 1969 ident: ref_122 article-title: Stabilization of Cowell’s method publication-title: Numer. Math. doi: 10.1007/BF02163234 – volume: 46 start-page: 560 year: 2023 ident: ref_48 article-title: A trigonometrically adapted 6(4) explicit Runge-Kutta-Nyström pair to solve oscillating systems publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.8528 – volume: 30 start-page: 1 year: 1990 ident: ref_126 article-title: High-order P-stable multistep methods publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(90)90001-G – volume: 31 start-page: 85 year: 1996 ident: ref_11 article-title: Embedded methods for the numerical solution of the Schrödinger equation publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(95)00196-4 – volume: 173 start-page: 389 year: 2005 ident: ref_36 article-title: Stability of explicit ARKN Methods for perturbed oscillators publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2004.05.017 – volume: 6 start-page: 19 year: 1980 ident: ref_54 article-title: A family of embedded Runge-Kutta formulae publication-title: J. Comput. Appl. Math. doi: 10.1016/0771-050X(80)90013-3 – volume: 28 start-page: 427 year: 1983 ident: ref_81 article-title: Exponentially-Fitted Solutions of the Eigenvalue Shrödinger Equation with Automatic Error Control publication-title: Comput. Phys. Commun. doi: 10.1016/0010-4655(83)90036-X – volume: 73 start-page: 306 year: 1987 ident: ref_68 article-title: Numerov Method Maximally Adapted to the Schrödinger-Equation publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(87)90139-2 – volume: 17 start-page: 663 year: 2006 ident: ref_94 article-title: A phase-fitted and amplification-fitted explicit two-Step hybrid Method for second-order periodic initial value problems publication-title: Int. J. Mod. Phys. doi: 10.1142/S0129183106009394 – volume: 184 start-page: 442 year: 2005 ident: ref_40 article-title: Frequency evaluation for exponentially fitted Runge-Kutta Methods publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2005.01.020 – volume: 189 start-page: 178 year: 2007 ident: ref_96 article-title: A trigonometrically fitted explicit hybrid Method for the numerical integration of orbital problems publication-title: Appl. Math. Comput. – volume: 100 start-page: 1694 year: 1990 ident: ref_10 article-title: Symmetric multistep methods for the numerical integration of planetary orbits publication-title: Astron. J. doi: 10.1086/115629 – volume: 97 start-page: 85 year: 2020 ident: ref_53 article-title: An explicit trigonometrically fitted Runge-Kutta method for stiff and oscillatory problems with two frequencies publication-title: Int. J. Comput. Math. doi: 10.1080/00207160.2018.1437263 – volume: 175 start-page: 241 year: 2006 ident: ref_105 article-title: Trigonometrically-fitted Method for a periodic initial value problem with two frequencies publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2006.03.004 – volume: 169 start-page: 171 year: 2004 ident: ref_106 article-title: The various order explicit multistep exponential fitting for systems of ordinary differential equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2003.12.015 – volume: 183 start-page: 2499 year: 2012 ident: ref_109 article-title: Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2012.06.013 – volume: 392 start-page: 113312 year: 2021 ident: ref_120 article-title: Two-frequency trigonometrically-fitted and symmetric linear multi-step methods for second-order oscillators publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2020.113312 – volume: 44 start-page: 95 year: 1987 ident: ref_80 article-title: Exponential and Bessel Fitting Methods for the Numerical-Solution of the Schrödinger-Equation publication-title: Comput. Phys. Commun. doi: 10.1016/0010-4655(87)90020-8 – volume: 53 start-page: 1339 year: 2007 ident: ref_95 article-title: An explicit Numerov-type Method for second-order differential equations with oscillating solutions publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2006.06.012 – volume: 31 start-page: 160 year: 1991 ident: ref_112 article-title: A four-step phase-fitted method for the numerical integration of second order initial-value problems publication-title: BIT Numer. Math. doi: 10.1007/BF01952791 – volume: 184 start-page: 1310 year: 2013 ident: ref_25 article-title: Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström Methods of explicit type publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2012.12.018 – volume: 21 start-page: 219 year: 2023 ident: ref_43 article-title: A New Phase- and Amplification-Fitted Sixth-Order Explicit RKN Method to Solve Oscillating Systems publication-title: Thai J. Math. – volume: 34 start-page: 36 year: 2023 ident: ref_114 article-title: A trigonometrically fitted intra-step block Falkner method for the direct integration of second-order delay differential equations with oscillatory solutions publication-title: Afr. Mat. doi: 10.1007/s13370-023-01075-3 – volume: 1 start-page: 143 year: 2001 ident: ref_17 article-title: On the construction of Exponentially-Fitted Methods for the Numerical Solution of the Schrödinger Equation publication-title: J. Comput. Meth. Sci. Eng. – volume: 232 start-page: 643 year: 2014 ident: ref_91 article-title: Trigonometrically fitted nonlinear two-Step Methods for solving second order oscillatory IVPs publication-title: Appl. Math. Comput. – volume: 260 start-page: 482 year: 2014 ident: ref_24 article-title: Symplectic explicit Methods of Runge-Kutta-Nyström type for solving perturbed oscillators publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2013.10.015 – volume: 173 start-page: 155 year: 2005 ident: ref_107 article-title: The arbitrary order implicit multistep schemes of exponential fitting and their applications publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2004.03.003 – ident: ref_8 – volume: 47 start-page: 871 year: 2010 ident: ref_100 article-title: A new two-Step hybrid Method for the numerical solution of the Schrödinger equation publication-title: J. Math. Chem. doi: 10.1007/s10910-009-9606-5 – volume: 188 start-page: 309 year: 2006 ident: ref_22 article-title: On the Generation of P-Stable Exponentially Fitted Runge-Kutta-Nyström Methods By Exponentially Fitted Runge-Kutta Methods publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2005.04.028 – volume: 72 start-page: 345 year: 1996 ident: ref_12 article-title: A generator of high-order embedded P-stable method for the numerical solution of the Schrödinger equation publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(96)00005-2 – volume: 178 start-page: 732 year: 2008 ident: ref_32 article-title: Sixth-order symmetric and symplectic exponentially fitted modified Runge-Kutta Methods of Gauss type publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2008.01.046 – volume: 18 start-page: 419 year: 2007 ident: ref_110 article-title: A P-stable eighteenth-order six-Step Method for periodic initial value problems publication-title: Int. J. Mod. Phys. doi: 10.1142/S0129183107010449 – volume: 23 start-page: 1378 year: 2010 ident: ref_129 article-title: On the frequency choice in trigonometrically fitted methods publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2010.07.003 – volume: 19 start-page: 23 year: 1980 ident: ref_76 article-title: A Numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies publication-title: Comput. Phys. Commun. doi: 10.1016/0010-4655(80)90062-4 – volume: 53 start-page: 473 year: 1995 ident: ref_13 article-title: Predictor-corrector phase-fitted methods for y′′ = f(x,y) and an application to the Schrödinger equation publication-title: Int. J. Quantum Chem. doi: 10.1002/qua.560530504 – volume: 72 start-page: 605 year: 2023 ident: ref_46 article-title: On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystr|"rom method with application to two-body problem publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2023.04.026 – volume: 10 start-page: 65 year: 1972 ident: ref_14 article-title: Chebyshevian multistep methods for ordinary differential equations publication-title: Numer. Math. doi: 10.1007/BF01395931 – volume: 44 start-page: 11 year: 1987 ident: ref_67 article-title: Coleman Method Maximally Adapted to the Schrödinger-Equation publication-title: Comput. Phys. Commun. doi: 10.1016/0010-4655(87)90013-0 – ident: ref_44 doi: 10.3390/math9030232 – ident: ref_131 – volume: 18 start-page: 455 year: 1981 ident: ref_128 article-title: An efficient numerical method for highly oscillatory ordinary differential equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/0718030 – volume: 177 start-page: 479 year: 2007 ident: ref_33 article-title: Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2007.05.003 – volume: 42 start-page: 873 year: 2005 ident: ref_38 article-title: Symplectic conditions for exponential fitting Runge-Kutta-Nyström Methods publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2005.09.015 – volume: 9 start-page: 145 year: 1989 ident: ref_64 article-title: Numerical-Methods for Y′′ = F(X,Y) Via Rational-Approximations for the Cosine publication-title: Ima J. Numer. Anal. doi: 10.1093/imanum/9.2.145 – ident: ref_7 – volume: 58 start-page: 341 year: 2008 ident: ref_86 article-title: A Trigonometrically Fitted Explicit Numerov-Type Method for Second-Order Initial Value Problems with Oscillating Solutions publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2006.12.003 – volume: 31 start-page: 843 year: 2023 ident: ref_47 article-title: Efficient Frequency-Dependent Coefficients of Explicit Improved Two-Derivative Runge-Kutta Type Methods for Solving Third- Order IVPs publication-title: Pertanika J. Sci. Technol. doi: 10.47836/pjst.31.2.10 – volume: 17 start-page: 365 year: 1987 ident: ref_63 article-title: An Explicit 6Th-Order Method with Phase-Lag of Order 8 for Y′′ = F(T, Y) publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(87)90113-0 – volume: 44 start-page: 1441 year: 2006 ident: ref_108 article-title: Truncation Errors in exponential fitting for oscillatory problems publication-title: Siam J. Numer. Anal. doi: 10.1137/050641752 – volume: 68 start-page: 1449 year: 2022 ident: ref_51 article-title: Exponentially-fitted and trigonometrically-fitted implicit RKN methods for solving y” = f (t, y) publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-021-01575-0 – volume: 16 start-page: 179 year: 1996 ident: ref_65 article-title: P-Stability and Exponential-Fitting Methods for Y′′ = F(X, Y) publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/16.2.179 – volume: 140 start-page: 423 year: 2002 ident: ref_130 article-title: Frequency evaluation in exponential fitting multistep algorithms for ODEs publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(01)00474-5 – volume: 24 start-page: 1 year: 1981 ident: ref_83 article-title: On the Numerical-Solution of the Schrödinger-Equation publication-title: Comput. Phys. Commun. doi: 10.1016/0010-4655(81)90101-6 – volume: 15 start-page: 253 year: 2021 ident: ref_52 article-title: Improved Runge-Kutta Method with Trigonometrically-Fitting Technique for Solving Oscillatory Problem publication-title: Malays. J. Math. Sci. – volume: 25 start-page: 113 year: 1984 ident: ref_4 article-title: Exponential multistep methods for ordinary differential equations publication-title: Bull. Greek Math. Soc. – ident: ref_18 – volume: 161 start-page: 283 year: 2003 ident: ref_56 article-title: A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2003.03.002 – volume: 66 start-page: 299 year: 1998 ident: ref_71 article-title: Exponential-Fitted Four-Step Methods for Y′′ = F(X,Y) publication-title: Int. J. Comput. Math. doi: 10.1080/00207169808804642 – volume: 185 start-page: 2527 year: 2014 ident: ref_90 article-title: Optimization of explicit two-Step hybrid Methods for solving orbital and oscillatory problems publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2014.05.030 – volume: 49 start-page: 1330 year: 2011 ident: ref_93 article-title: A hybrid Method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation publication-title: J. Math. Chem. doi: 10.1007/s10910-011-9824-5 – volume: 16 start-page: 739 year: 2022 ident: ref_115 article-title: Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory Solutions publication-title: Malays. J. Math. Sci. doi: 10.47836/mjms.16.4.07 – volume: 461 start-page: 1639 year: 2005 ident: ref_102 article-title: An improved trigonometrically fitted P-stable Obrechkoff Method for periodic initial-value problems publication-title: Proc. R. Soc. Math. Phys. Eng. Sci. – ident: ref_119 doi: 10.3390/math9080806 – ident: ref_121 doi: 10.3390/math7121197 – volume: 24 start-page: 241 year: 1980 ident: ref_84 article-title: Exponential-Fitting Methods for the Numerical-Integration of the 4Th-Order Differential-Equation Yiv + F·Y = G publication-title: Computing doi: 10.1007/BF02281728 – volume: 536 start-page: 75 year: 2014 ident: ref_57 article-title: Runge–Kutta type methods with special properties for the numerical integration of ordinary differential equations publication-title: Phys. Rep. doi: 10.1016/j.physrep.2013.11.003 – volume: 100 start-page: 56 year: 1997 ident: ref_69 article-title: Four-Step Exponential-Fitted Methods for Nonlinear Physical Problems publication-title: Comput. Phys. Commun. doi: 10.1016/S0010-4655(96)00147-6 – volume: 7 start-page: 235 year: 1987 ident: ref_20 article-title: Families of Runge-Kutta-Nyström formulae publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/7.2.235 – volume: 59 start-page: 815 year: 2009 ident: ref_87 article-title: Exponentially-fitted Obrechkoff Methods for second-order differential equations publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2008.03.018 |
| SSID | ssj0000913849 |
| Score | 2.3371277 |
| Snippet | In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we... |
| SourceID | doaj proquest gale crossref |
| SourceType | Open Website Aggregation Database Enrichment Source Index Database |
| StartPage | 504 |
| SubjectTerms | Adams–Bashforth methods Algebra Algorithms Bibliographic literature Boundary value problems Comparative analysis initial value problems (IVPs) Methods multistep methods numerical solution Stability analysis trigonometric fitting |
| SummonAdditionalLinks | – databaseName: Computer Science Database (ProQuest) dbid: K7- link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwELZKywEOUF5ioa18AHFAVp04XjsntKCuWpU-DoB6s-yJXZCq3WWz8PuZ8XpDL-XCMck4SjTjefsbxt50USbZBi2kb4NolJEioJkQlbW-TmgBLWQQ18_m_NxeXbWXJeHWl7bKjU7MirqbA-XID9EsSSpB1e2HxU9BU6OoulpGaNxjO1Vd5415asSQYyHMS9u06353hdH9IXqB36saBVeXyWwbS5QB--9Sy9nWTB__71fuskfFy-STtVg8YVtx9pQ9PBsgWvtnbDXhqOD4WZ4gnXPrHP1XjhT8ViMRnyd-lFEm6CKf1kWxWJRlfV4y_YEepLggDE9-8u2y55Tb5RdoW2-o0W52zYfc23P2dXr05dOxKCMYBKClXwnfGAlajiPEFKoUbPLeVB1g4ON10FXq0liGUMVkFbQpVV0DkYqzSUOwyqsXbHs2n8WXjGtV606FaMMYY1KAoDRoLxO-wxoj6xF7v2GHg4JPTmMybhzGKcQ8d5t5I_Z2oF6scTnuoPtInB1oCE0735gvr13ZnE4FgES6K9nY-K4NMfmma4wGQ4XQOGLvSC4c7Xn8JPDl6AL-GKFnuQkVbym4G4_Y3kYuXFEGvfsrFK_-_fg1e1Cjz7RuCt9j26vlr7jP7sNv5O3yIMv2H0jCBbw priority: 102 providerName: ProQuest |
| Title | A New Methodology for the Development of Efficient Multistep Methods for First-Order IVPs with Oscillating Solutions |
| URI | https://www.proquest.com/docview/2930979929 https://doaj.org/article/3bccf2578f8e4ad9befa4d475c70529e |
| Volume | 12 |
| WOSCitedRecordID | wos001169804000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: DOA dateStart: 20130101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: M~E dateStart: 20130101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: Computer Science Database (ProQuest) customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: K7- dateStart: 20130301 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: M7S dateStart: 20130301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest - Publicly Available Content Database customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: PIMPY dateStart: 20130301 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 2227-7390 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913849 issn: 2227-7390 databaseCode: BENPR dateStart: 20130301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Lj9MwELbQwgEOiKcoLJUPIA7IWieOa_vYRa1YQbsRLy0ny57YC9Kqu9oWjvx2Zpy06mXFhUukJOPI8Yw9M57xN4y96pLM0kUtZHBRNMpIEVFNiMraUGfUgBYKiOtHs1zaszPX7pX6opywHh64H7gjFQEyyVW2qQmdiymHpmuMBkNBqkSrrzRuz5kqa7CrlG1cn-mu0K8_QvvvR1WjyOqhJttWBxWo_psW5KJl5g_Y_cE85NO-Ww_ZrbR6xO4tdtiq68dsM-W4MvFFKf1cNsU5Gp4cKfheBhC_zHxW4CHophyzRX5eDc3Wpcn8J5p-4pTAN_nJt3bNaVOWn6JSvKAMudU5322aPWFf57Mv796LoXaCAFTRGxEaI0HLSYKUY5WjzSGYqgP0WIKOuspdnsgYq5StApdz1TWQKKqaNUSrgnrKDlaXq_SMca1q3amYbJygMwkQlQYdZMZvWGNkPWJvt6PpYQAWp_oWFx4dDBp7vz_2I_Z6R33VA2rcQHdMjNnREAx2eYDC4Qfh8P8SjhF7Q2z1NFmxSxCGMwf4YwR75acUdSWvbDJih1vO-2EWrz2aQpLCnrV7_j9684LdrdEk6nO-D9nB5vpXesnuwG-UgOsxu308W7afxkWQ8frBiDFlon6m658Zvm9PFu33v4gx_1M |
| linkProvider | Directory of Open Access Journals |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3Nb9MwFH8aHRJw4BtRGOADEwcUzYnjxjkg1EGrVWu7Cg20m7Ede5s0taUpIP4p_kbey0fZZdx24JjEjuL45_fh9_x7AK8LzwPPrYy4yW2UioxHFtVEFCtlkoAaULmKxHWcTafq5CSfbcHv9iwMpVW2MrES1MXC0R75HqolTiGoJH-__BZR1SiKrrYlNGpYHPpfP9FlK9-NPuL87ibJcHD84SBqqgpEDpXXOjJpxp3kPe98sHGwKhiTxYVDW95IK-NQhB63NvZBCZeHEBep8xRvDNJZJYzA996A7VSkadKB7f3BdPZps6tDLJsqzesMeyFyvod251mc4FKRTS24VvdVJQKuUgSVdhve-9_-y32429jRrF8D_wFs-flDuDPZkNCWj2DdZyjC2aSqkV1FDxha6AxbsEupUmwR2KDi0aCL6jwyAn_ZdCurLsNztJGjI2IpZaMvs5LR7jU7QuvhglIJ56dss7v4GD5fy7CfQGe-mPunwKRIZCGsV7aHXrdzVkgnDQ_4DpVlPOnC23b6tWsY2KkQyIVGT4zAoi-DpQu7m9bLmnnkinb7hKRNG-ILr24sVqe6ET9aWOcCSeegfGqK3Ppg0iLNpMso1Ou78IZwqEmq4Sc50xzOwIERP5juU3ia3NdeF3ZaHOpG3JX6Lwif_fvxK7h1cDwZ6_FoevgcbidoIdYp8DvQWa---xdw0_3AeV69bFYWg6_XDdo_zv5o6w |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwEB6VghAceKMuFPCBigOK1onjjXNAaKFdsWq7XYmHenNtxy6Vqt1ls4D4a_w6ZrxJ6KXceuCYxI7i-PM8PONvAF5WngdeWplwU9okFwVPLKqJJFXKZAE1oHKRxPWgmEzU8XE53YDf7VkYSqtsZWIU1NXc0R55H9USpxBUVvZDkxYx3R29XXxLqIIURVrbchpriOz7Xz_RfavfjHdxrneybLT36f2HpKkwkDhUZKvE5AV3kg-888GmwapgTJFWDu16I61MQxUG3NrUByVcGUJa5c5T7DFIZ5UwAt97Da4XuVRpTBv82O3vEN-myst1rr0QJe-jBfo1zXDRyKYqXKsFY7GAy1RC1HOju__zH7oHdxrrmg3Xy-E-bPjZA7h92FHT1g9hNWQo2NlhrJwdYwoM7XaGLdiFBCo2D2wvsmvQRTyljMth0XSrY5fRGVrOyRFxl7Lxl2nNaE-bHaFNcU4JhrNT1u05PoLPVzLsx7A5m8_8FjApMlkJ65UdoC_unBXSScMDvkMVBc968LqFgnYNLzuVBznX6J8RcPRF4PRgp2u9WPORXNLuHaGqa0Ms4vHGfHmqG6GkhXUukMwOyuemKq0PJq_yQrqCAsC-B68Ik5pkHX6SM82RDRwYsYbpIQWtyakd9GC7xaRuhGCt_wLyyb8fv4CbiFR9MJ7sP4VbGZqN67z4bdhcLb_7Z3DD_cBpXj6PS4zByVUj9g-IsHBt |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+New+Methodology+for+the+Development+of+Efficient+Multistep+Methods+for+First-Order+IVPs+with+Oscillating+Solutions&rft.jtitle=Mathematics+%28Basel%29&rft.au=Simos%2C+Theodore+E&rft.date=2024-02-01&rft.pub=MDPI+AG&rft.issn=2227-7390&rft.eissn=2227-7390&rft.volume=12&rft.issue=4&rft_id=info:doi/10.3390%2Fmath12040504&rft.externalDocID=A784102176 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2227-7390&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2227-7390&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2227-7390&client=summon |