Numerical algorithms for diffusion–reaction problems with non-classical conditions
Parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years. In this paper new high-order algorithms for the linear diffusion–reaction problem are derived. The convergence of the new schemes is studied and numerical examples are given to show the effi...
Gespeichert in:
| Veröffentlicht in: | Applied mathematics and computation Jg. 218; H. 9; S. 5487 - 5495 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier Inc
2012
|
| Schlagworte: | |
| ISSN: | 0096-3003, 1873-5649 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years. In this paper new high-order algorithms for the linear diffusion–reaction problem are derived. The convergence of the new schemes is studied and numerical examples are given to show the efficiency of the new methods to solve linear and nonlinear diffusion–reaction equations with these non classical conditions. |
|---|---|
| AbstractList | Parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years. In this paper new high-order algorithms for the linear diffusion-reaction problem are derived. The convergence of the new schemes is studied and numerical examples are given to show the efficiency of the new methods to solve linear and nonlinear diffusion-reaction equations with these non classical conditions. |
| Author | Queiruga-Dios, A. Martín-Vaquero, J. Encinas, A.H. |
| Author_xml | – sequence: 1 givenname: J. surname: Martín-Vaquero fullname: Martín-Vaquero, J. email: jesmarva@usal.es – sequence: 2 givenname: A. surname: Queiruga-Dios fullname: Queiruga-Dios, A. email: queirugadios@usal.es – sequence: 3 givenname: A.H. surname: Encinas fullname: Encinas, A.H. email: ascen@usal.es |
| BookMark | eNp9kL1OwzAURi1UJNrCA7BlZEmw4yROxIQq_qQKlu6Wc22DKycudgJi4x14Q54EhzIxVLrS9XCO9d1vgWa96xVC5wRnBJPqcpuJDrIcE5LFwZQdoTmpGU3LqmhmaI5xU6UUY3qCFiFsMcasIsUcbR7HTnkDwibCPjtvhpcuJNr5RBqtx2Bc__355ZWAIT6TnXetVZF4j2ASM6RgRQi_PrhemokKp-hYCxvU2d9eos3tzWZ1n66f7h5W1-sUKMVD2la0rRvWqJxIKSDXNGekzKEuBADTGloiQUhdaKpLJppKy0YwyEUhVUlqukQX-29jqtdRhYF3JoCyVvTKjYHHYnBdk7giyvYoeBeCV5qDGcQUdvDC2IhOdMW3PNbIpxp5nFhjNMk_c-dNJ_zHQedq76h4_JtRngcwqgcljVcwcOnMAfsHgtiQeg |
| CitedBy_id | crossref_primary_10_1155_2013_959216 crossref_primary_10_1002_fld_70010 crossref_primary_10_1155_2012_846582 crossref_primary_10_1016_j_amc_2016_07_003 crossref_primary_10_3846_mma_2020_8023 crossref_primary_10_1016_j_amc_2018_09_025 crossref_primary_10_1080_00036811_2017_1359558 crossref_primary_10_1080_00207721_2025_2536210 crossref_primary_10_1186_1687_2770_2012_80 crossref_primary_10_1155_2012_230190 crossref_primary_10_1007_s10013_014_0113_z crossref_primary_10_1007_s11075_016_0192_x crossref_primary_10_1016_j_amc_2015_03_039 crossref_primary_10_1155_2012_237657 crossref_primary_10_1002_num_22411 |
| Cites_doi | 10.1155/2008/904824 10.32917/hmj/1206126957 10.1016/j.camwa.2005.05.005 10.1016/j.cnsns.2009.01.013 10.1090/qam/693879 10.1090/qam/1178432 10.1016/0362-546X(92)90148-8 10.1016/j.apnum.2004.02.002 10.1016/j.apm.2011.10.021 10.1081/NFA-200041711 10.1090/qam/678203 10.1016/j.cam.2009.04.016 10.1016/0167-2789(90)90142-C 10.1016/0167-2789(83)90130-6 10.1017/S0027763000020754 10.1016/j.na.2007.02.006 10.1016/S0377-0427(00)00614-2 10.1016/S0362-546X(97)00269-1 10.1155/S1026022604403033 10.1016/j.amc.2011.03.155 10.1016/j.apnum.2008.07.001 10.1016/j.chaos.2009.03.122 10.1016/j.cam.2009.01.012 10.1016/S0377-0427(97)00215-X 10.1016/S0362-546X(01)00479-5 10.1002/num.20230 10.1016/S0362-546X(96)00003-X |
| ContentType | Journal Article |
| Copyright | 2011 Elsevier Inc. |
| Copyright_xml | – notice: 2011 Elsevier Inc. |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| DOI | 10.1016/j.amc.2011.11.037 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1873-5649 |
| EndPage | 5495 |
| ExternalDocumentID | 10_1016_j_amc_2011_11_037 S0096300311013671 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 23M 4.4 457 4G. 5GY 5VS 6J9 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABFRF ABJNI ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFO ACGFS ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD AEBSH AEFWE AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AI. AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HLZ HMJ HVGLF HZ~ IHE J1W KOM LG9 M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ RXW SBC SDF SDG SES SEW SME SPC SPCBC SSW SSZ T5K TAE TN5 VH1 VOH WH7 WUQ X6Y XPP ZMT ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c330t-b63b8979e21ddac2f327152c84acc7ffcb1dcadf4f3f57a96fd9a7c2a4de5183 |
| ISICitedReferencesCount | 27 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000298293200074&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0096-3003 |
| IngestDate | Sat Sep 27 22:03:08 EDT 2025 Sat Nov 29 06:12:27 EST 2025 Tue Nov 18 21:02:24 EST 2025 Fri Feb 23 02:31:13 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 9 |
| Keywords | Explicit technique Diffusion–reaction problem Numerical examples Non-classic boundary value problems Convergence |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c330t-b63b8979e21ddac2f327152c84acc7ffcb1dcadf4f3f57a96fd9a7c2a4de5183 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 1010881101 |
| PQPubID | 23500 |
| PageCount | 9 |
| ParticipantIDs | proquest_miscellaneous_1010881101 crossref_citationtrail_10_1016_j_amc_2011_11_037 crossref_primary_10_1016_j_amc_2011_11_037 elsevier_sciencedirect_doi_10_1016_j_amc_2011_11_037 |
| PublicationCentury | 2000 |
| PublicationDate | 2012 2012-1-00 20120101 |
| PublicationDateYYYYMMDD | 2012-01-01 |
| PublicationDate_xml | – year: 2012 text: 2012 |
| PublicationDecade | 2010 |
| PublicationTitle | Applied mathematics and computation |
| PublicationYear | 2012 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Day (b0065) 1982; 40 Ashyralyev, Yurtsever (b0030) 2001; 47 Mesloub (b0125) 2008; 68 Martín-Vaquero (b0110) 2009; 42 Chabrowski (b0050) 1984; 93 Diaz (b0090) 1997; 30 Strikwerda (b0155) 2004 Gordeziani, Natalini, Ricci (b0100) 2005; 50 Martín-Vaquero, Wade (b0120) 2011 Zhou, Cui, Lin (b0160) 2009; 230 Dehghan (b0085) 2005; 52 Bouziani (b0040) 1999; 10 Day (b0075) 1985 Pao (b0130) 1998; 88 Samarskii (b0145) 1980; 16 Bishop, Fesser, Lomdahl, Kerr, Willams, Tullinger (b0035) 1983; 7 Pao (b0135) 2001; 136 Ashyralyev, Aggez (b0005) 2004; 25 Choi, Chan (b0055) 1992; 18 Ashyralyev, Gercek (b0010) 2008 Day (b0070) 1983; 41 Ercolani, Forest, Mclaughlin (b0095) 1990; 43 Bouziani (b0045) 1997; 27 Ramezani, Dehghan, Razzaghi (b0140) 2007; 24 Ashyralyev, Karatay, Sobolevskii (b0015) 2004 Martín-Vaquero, Vigo-Aguiar (b0115) 2009; 59 Ashyralyev, Yildirim (b0025) 2011; 218 Slodicka, Dehilis (b0150) 2009; 231 Ashyralyev, Ozdemir (b0020) 2005; 12 Day (b0080) 1992; 50 Lepin, Myshkis (b0105) 1997; 28 Dai, Xian (b0060) 2009; 14 Dai (10.1016/j.amc.2011.11.037_b0060) 2009; 14 Ashyralyev (10.1016/j.amc.2011.11.037_b0005) 2004; 25 Day (10.1016/j.amc.2011.11.037_b0080) 1992; 50 Mesloub (10.1016/j.amc.2011.11.037_b0125) 2008; 68 Strikwerda (10.1016/j.amc.2011.11.037_b0155) 2004 Zhou (10.1016/j.amc.2011.11.037_b0160) 2009; 230 Choi (10.1016/j.amc.2011.11.037_b0055) 1992; 18 Bishop (10.1016/j.amc.2011.11.037_b0035) 1983; 7 Lepin (10.1016/j.amc.2011.11.037_b0105) 1997; 28 Slodicka (10.1016/j.amc.2011.11.037_b0150) 2009; 231 Pao (10.1016/j.amc.2011.11.037_b0130) 1998; 88 Ashyralyev (10.1016/j.amc.2011.11.037_b0025) 2011; 218 Bouziani (10.1016/j.amc.2011.11.037_b0045) 1997; 27 Samarskii (10.1016/j.amc.2011.11.037_b0145) 1980; 16 Day (10.1016/j.amc.2011.11.037_b0070) 1983; 41 Bouziani (10.1016/j.amc.2011.11.037_b0040) 1999; 10 Ercolani (10.1016/j.amc.2011.11.037_b0095) 1990; 43 Martín-Vaquero (10.1016/j.amc.2011.11.037_b0110) 2009; 42 Chabrowski (10.1016/j.amc.2011.11.037_b0050) 1984; 93 Martín-Vaquero (10.1016/j.amc.2011.11.037_b0120) 2011 Ramezani (10.1016/j.amc.2011.11.037_b0140) 2007; 24 Ashyralyev (10.1016/j.amc.2011.11.037_b0030) 2001; 47 Dehghan (10.1016/j.amc.2011.11.037_b0085) 2005; 52 Pao (10.1016/j.amc.2011.11.037_b0135) 2001; 136 Day (10.1016/j.amc.2011.11.037_b0065) 1982; 40 Gordeziani (10.1016/j.amc.2011.11.037_b0100) 2005; 50 Diaz (10.1016/j.amc.2011.11.037_b0090) 1997; 30 Ashyralyev (10.1016/j.amc.2011.11.037_b0020) 2005; 12 Martín-Vaquero (10.1016/j.amc.2011.11.037_b0115) 2009; 59 Ashyralyev (10.1016/j.amc.2011.11.037_b0010) 2008 Ashyralyev (10.1016/j.amc.2011.11.037_b0015) 2004 Day (10.1016/j.amc.2011.11.037_b0075) 1985 |
| References_xml | – volume: 27 start-page: 373 year: 1997 end-page: 390 ident: b0045 article-title: Strong solution for a mixed problem with nonlocal condition for a certain pluriparabolic equations publication-title: Hiroshima Math. J. – volume: 52 start-page: 39 year: 2005 end-page: 62 ident: b0085 article-title: Efficient techniques for the second-order parabolic equation subject to nonlocal specifications publication-title: Appl. Numer. Math. – volume: 136 start-page: 227 year: 2001 end-page: 243 ident: b0135 article-title: Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions publication-title: J. Comput. Appl. Math. – year: 2004 ident: b0155 article-title: Finite Difference Schemes and Partial Differential Equations – volume: 18 start-page: 317 year: 1992 end-page: 331 ident: b0055 article-title: A parabolic equation with nonlocal boundary condition arising from electrochemistry publication-title: Nonlinear Anal. Theory Methods Appl. – volume: 93 start-page: 109 year: 1984 end-page: 131 ident: b0050 article-title: On nonlocal problems for parabolic equations publication-title: Nagaya Math. J. – volume: 7 start-page: 259 year: 1983 end-page: 279 ident: b0035 article-title: Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system publication-title: Phys. D: Nonlinear Phenom. – volume: 28 start-page: 1533 year: 1997 end-page: 1543 ident: b0105 article-title: General nonlocal nonlinear boundary value problem for differential equation of 3rd order publication-title: Nonlinear Anal. – volume: 25 start-page: 439 year: 2004 end-page: 462 ident: b0005 article-title: A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations publication-title: Numer. Funct. Anal. Optim. – volume: 10 start-page: 61 year: 1999 end-page: 77 ident: b0040 article-title: On a class of parabolic equations with a nonlocal boundary condition publication-title: Acad. Roy. Belg. Bull. Cl. Sci. – year: 2011 ident: b0120 article-title: On efficient numerical methods for an initial-boundary value problem with nonlocal boundary conditions publication-title: Appl. Math. Model. – volume: 88 start-page: 225 year: 1998 end-page: 238 ident: b0130 article-title: Asymptotic behavior of solutions of reaction–diffusion equations with nonlocal boundary conditions publication-title: J. Comput. Appl. Math. – volume: 59 start-page: 1258 year: 2009 end-page: 1264 ident: b0115 article-title: A note on efficient techniques for the second-order parabolic equation subject to non-local conditions publication-title: Appl. Numer. Math. – volume: 43 start-page: 349 year: 1990 end-page: 384 ident: b0095 article-title: Geometry of the modulational instability: III. Homoclinic orbits for the periodic sine-Gordon equation publication-title: Phys. D – volume: 14 start-page: 3239 year: 2009 end-page: 3249 ident: b0060 article-title: Homoclinic breather-wave solutions for Sine-Gordon equation publication-title: Commun. Nonlinear Sci. Numer. Simulat. – volume: 68 start-page: 2594 year: 2008 end-page: 2607 ident: b0125 article-title: On a singular two dimensional nonlinear evolution equation with nonlocal conditions publication-title: Nonlinear Anal.: Theory, Methods Appl. – volume: 50 start-page: 523 year: 1992 end-page: 533 ident: b0080 article-title: Parabolic equations and thermodynamics publication-title: Quart. Appl. Math – volume: 218 start-page: 1124 year: 2011 end-page: 1131 ident: b0025 article-title: Stable difference schemes for the hyperbolic problems subject to nonlocal boundary conditions with self-adjoint operator publication-title: Appl. Math. Comput. – volume: 41 start-page: 468 year: 1983 end-page: 475 ident: b0070 article-title: A decreasing property of solutions of a parabolic equation with applications to thermoelasticity and other theories publication-title: Quart. Appl. Math. – volume: 16 start-page: 1221 year: 1980 end-page: 1228 ident: b0145 article-title: Some problems in differential equations theory publication-title: Differ. Equat. – volume: 231 start-page: 715 year: 2009 end-page: 724 ident: b0150 article-title: A numerical approach for a semilinear parabolic equation with a nonlocal boundary condition publication-title: J. Comput. Appl. Math. – year: 1985 ident: b0075 article-title: Heat Conduction within Linear Thermoelasticity – volume: 50 start-page: 1333 year: 2005 end-page: 1344 ident: b0100 article-title: Finite-difference methods for solution of nonlocal boundary value problems publication-title: Comput. Math. Appl. – volume: 42 start-page: 2364 year: 2009 end-page: 2372 ident: b0110 article-title: Two-level fourth-order explicit schemes for diffusion equations subject to boundary integral specifications publication-title: Chaos, Solitons Fractals – volume: 230 start-page: 770 year: 2009 end-page: 780 ident: b0160 article-title: Numerical algorithm for parabolic problems with non-classical conditions publication-title: J. Comput. Appl. Math. – volume: 24 start-page: 1 year: 2007 end-page: 8 ident: b0140 article-title: Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition publication-title: Numerical Methods PDEs – volume: 12 start-page: 67 year: 2005 end-page: 81 ident: b0020 article-title: A note on the nonlocal boundary value problem for hyperbolic–parabolic equations publication-title: Funct. Differ. Equat. – volume: 47 start-page: 3585 year: 2001 end-page: 3592 ident: b0030 article-title: On a nonlocal boundary value problem for semilinear hyperbolic–parabolic equations publication-title: Nonlinear Anal. – start-page: 273 year: 2004 end-page: 286 ident: b0015 article-title: On well-posedness of the nonlocal boundary value problem for parabolic difference equations publication-title: Disc. Dyn. Nature Soc. – volume: 40 start-page: 319 year: 1982 end-page: 330 ident: b0065 article-title: Existence of a property of solutions of the heat equation subject to linear thermoelasticity and other theories publication-title: Quart. Appl. Math. – volume: 30 start-page: 3963 year: 1997 end-page: 3974 ident: b0090 article-title: On a nonlocal elliptic problem arising in the magnetic confinement of a plasma in a stellarator publication-title: Nonlinear Anal. – start-page: 1 year: 2008 end-page: 16 ident: b0010 article-title: Nonlocal boundary value problems for elliptic–parabolic differential and difference equations publication-title: Disc. Dyn. Nature Soc. – volume: 10 start-page: 61 year: 1999 ident: 10.1016/j.amc.2011.11.037_b0040 article-title: On a class of parabolic equations with a nonlocal boundary condition publication-title: Acad. Roy. Belg. Bull. Cl. Sci. – start-page: 1 year: 2008 ident: 10.1016/j.amc.2011.11.037_b0010 article-title: Nonlocal boundary value problems for elliptic–parabolic differential and difference equations publication-title: Disc. Dyn. Nature Soc. doi: 10.1155/2008/904824 – year: 1985 ident: 10.1016/j.amc.2011.11.037_b0075 – volume: 27 start-page: 373 year: 1997 ident: 10.1016/j.amc.2011.11.037_b0045 article-title: Strong solution for a mixed problem with nonlocal condition for a certain pluriparabolic equations publication-title: Hiroshima Math. J. doi: 10.32917/hmj/1206126957 – volume: 50 start-page: 1333 year: 2005 ident: 10.1016/j.amc.2011.11.037_b0100 article-title: Finite-difference methods for solution of nonlocal boundary value problems publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2005.05.005 – year: 2004 ident: 10.1016/j.amc.2011.11.037_b0155 – volume: 14 start-page: 3239 year: 2009 ident: 10.1016/j.amc.2011.11.037_b0060 article-title: Homoclinic breather-wave solutions for Sine-Gordon equation publication-title: Commun. Nonlinear Sci. Numer. Simulat. doi: 10.1016/j.cnsns.2009.01.013 – volume: 41 start-page: 468 year: 1983 ident: 10.1016/j.amc.2011.11.037_b0070 article-title: A decreasing property of solutions of a parabolic equation with applications to thermoelasticity and other theories publication-title: Quart. Appl. Math. doi: 10.1090/qam/693879 – volume: 50 start-page: 523 year: 1992 ident: 10.1016/j.amc.2011.11.037_b0080 article-title: Parabolic equations and thermodynamics publication-title: Quart. Appl. Math doi: 10.1090/qam/1178432 – volume: 18 start-page: 317 year: 1992 ident: 10.1016/j.amc.2011.11.037_b0055 article-title: A parabolic equation with nonlocal boundary condition arising from electrochemistry publication-title: Nonlinear Anal. Theory Methods Appl. doi: 10.1016/0362-546X(92)90148-8 – volume: 52 start-page: 39 year: 2005 ident: 10.1016/j.amc.2011.11.037_b0085 article-title: Efficient techniques for the second-order parabolic equation subject to nonlocal specifications publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2004.02.002 – year: 2011 ident: 10.1016/j.amc.2011.11.037_b0120 article-title: On efficient numerical methods for an initial-boundary value problem with nonlocal boundary conditions publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2011.10.021 – volume: 25 start-page: 439 year: 2004 ident: 10.1016/j.amc.2011.11.037_b0005 article-title: A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations publication-title: Numer. Funct. Anal. Optim. doi: 10.1081/NFA-200041711 – volume: 40 start-page: 319 year: 1982 ident: 10.1016/j.amc.2011.11.037_b0065 article-title: Existence of a property of solutions of the heat equation subject to linear thermoelasticity and other theories publication-title: Quart. Appl. Math. doi: 10.1090/qam/678203 – volume: 231 start-page: 715 year: 2009 ident: 10.1016/j.amc.2011.11.037_b0150 article-title: A numerical approach for a semilinear parabolic equation with a nonlocal boundary condition publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2009.04.016 – volume: 43 start-page: 349 year: 1990 ident: 10.1016/j.amc.2011.11.037_b0095 article-title: Geometry of the modulational instability: III. Homoclinic orbits for the periodic sine-Gordon equation publication-title: Phys. D doi: 10.1016/0167-2789(90)90142-C – volume: 7 start-page: 259 year: 1983 ident: 10.1016/j.amc.2011.11.037_b0035 article-title: Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system publication-title: Phys. D: Nonlinear Phenom. doi: 10.1016/0167-2789(83)90130-6 – volume: 93 start-page: 109 year: 1984 ident: 10.1016/j.amc.2011.11.037_b0050 article-title: On nonlocal problems for parabolic equations publication-title: Nagaya Math. J. doi: 10.1017/S0027763000020754 – volume: 68 start-page: 2594 year: 2008 ident: 10.1016/j.amc.2011.11.037_b0125 article-title: On a singular two dimensional nonlinear evolution equation with nonlocal conditions publication-title: Nonlinear Anal.: Theory, Methods Appl. doi: 10.1016/j.na.2007.02.006 – volume: 136 start-page: 227 year: 2001 ident: 10.1016/j.amc.2011.11.037_b0135 article-title: Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(00)00614-2 – volume: 30 start-page: 3963 year: 1997 ident: 10.1016/j.amc.2011.11.037_b0090 article-title: On a nonlocal elliptic problem arising in the magnetic confinement of a plasma in a stellarator publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(97)00269-1 – volume: 16 start-page: 1221 year: 1980 ident: 10.1016/j.amc.2011.11.037_b0145 article-title: Some problems in differential equations theory publication-title: Differ. Equat. – start-page: 273 year: 2004 ident: 10.1016/j.amc.2011.11.037_b0015 article-title: On well-posedness of the nonlocal boundary value problem for parabolic difference equations publication-title: Disc. Dyn. Nature Soc. doi: 10.1155/S1026022604403033 – volume: 218 start-page: 1124 year: 2011 ident: 10.1016/j.amc.2011.11.037_b0025 article-title: Stable difference schemes for the hyperbolic problems subject to nonlocal boundary conditions with self-adjoint operator publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2011.03.155 – volume: 12 start-page: 67 year: 2005 ident: 10.1016/j.amc.2011.11.037_b0020 article-title: A note on the nonlocal boundary value problem for hyperbolic–parabolic equations publication-title: Funct. Differ. Equat. – volume: 59 start-page: 1258 year: 2009 ident: 10.1016/j.amc.2011.11.037_b0115 article-title: A note on efficient techniques for the second-order parabolic equation subject to non-local conditions publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2008.07.001 – volume: 42 start-page: 2364 year: 2009 ident: 10.1016/j.amc.2011.11.037_b0110 article-title: Two-level fourth-order explicit schemes for diffusion equations subject to boundary integral specifications publication-title: Chaos, Solitons Fractals doi: 10.1016/j.chaos.2009.03.122 – volume: 230 start-page: 770 year: 2009 ident: 10.1016/j.amc.2011.11.037_b0160 article-title: Numerical algorithm for parabolic problems with non-classical conditions publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2009.01.012 – volume: 88 start-page: 225 year: 1998 ident: 10.1016/j.amc.2011.11.037_b0130 article-title: Asymptotic behavior of solutions of reaction–diffusion equations with nonlocal boundary conditions publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(97)00215-X – volume: 47 start-page: 3585 year: 2001 ident: 10.1016/j.amc.2011.11.037_b0030 article-title: On a nonlocal boundary value problem for semilinear hyperbolic–parabolic equations publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(01)00479-5 – volume: 24 start-page: 1 year: 2007 ident: 10.1016/j.amc.2011.11.037_b0140 article-title: Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition publication-title: Numerical Methods PDEs doi: 10.1002/num.20230 – volume: 28 start-page: 1533 year: 1997 ident: 10.1016/j.amc.2011.11.037_b0105 article-title: General nonlocal nonlinear boundary value problem for differential equation of 3rd order publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(96)00003-X |
| SSID | ssj0007614 |
| Score | 2.1445258 |
| Snippet | Parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years. In this paper new high-order algorithms for the... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 5487 |
| SubjectTerms | Algorithms Boundary conditions Computational efficiency Convergence Diffusion Diffusion-reaction equations Diffusion–reaction problem Explicit technique Mathematical analysis Non-classic boundary value problems Nonlinearity Numerical examples |
| Title | Numerical algorithms for diffusion–reaction problems with non-classical conditions |
| URI | https://dx.doi.org/10.1016/j.amc.2011.11.037 https://www.proquest.com/docview/1010881101 |
| Volume | 218 |
| WOSCitedRecordID | wos000298293200074&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-5649 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0007614 issn: 0096-3003 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Ja9tAFB6M00N7KF1puqFCT4UxkkajkY6mcUkDNYWa4psYzUipQyIb2wo59j_kH_aX9D3NIju0oS30IsxYm-d9fvtCyNssklEueUgF14oC99O01JWkeY3CjTMpy6wbNiGm02w-zz8PBteuFubyXDRNdnWVr_4rqWENiI2ls39Bbn9TWIDPQHQ4Atnh-EeEn7YmCIOpx6dLsP2_mZ4L3SyUFp1jLsGBgcJoJoXbsTK21K1ZNlShVm27h2BU27v1XMdaq71e-LavG1cit2r3w_vYqaCLxx819KsEOWRKa05GO07Xxbo9lfRoYZL-xv6rSaMWjbSLx6NdH0XU27K-bGYvqxPtJsrC0HC2ynDeTDDKU9O_1LHmuOfNrcs-N4wWDa0doQ1WLv-lQDC-ibORvFCmXyu2bGWil34-J_ELvhW-FChE2McOTOqDWIC9NSQH44-T-YkX8CI1LePdr3DB8i5t8MaDfqfu3BD8nTYze0DuWzMkGBv4PCSDqnlE7n3qifmYzDyQgh5IAQAp8ED68f3aQShwEAoQQsEehIIeQk_I7MNk9v6Y2hkcVDEWbmmZsjLLRV7FkdZSxTWLBah8KkukUqKuVRlpJXWd1KzmQuZprXMpVCwTXXEQF0_JEJ5YPSMBmOpSZExVZVgnJdj5PEp1zbkENqJTLQ9J6HaqULY_PY5JOS9cIuJZAZtb4OaC3VrA5h6Sd_6SlWnOctvJidv-wmqXRmssACu3XfbGkaoAzovhNNlUy3aD54OIRrQ8_7dbvyB38c9iHHovyXC7bqtX5I663C4269cWdT8BQ5itlQ |
| linkProvider | Elsevier |
| 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=Numerical+algorithms+for+diffusion%E2%80%93reaction+problems+with+non-classical+conditions&rft.jtitle=Applied+mathematics+and+computation&rft.au=Mart%C3%ADn-Vaquero%2C+J.&rft.au=Queiruga-Dios%2C+A.&rft.au=Encinas%2C+A.H.&rft.date=2012&rft.pub=Elsevier+Inc&rft.issn=0096-3003&rft.eissn=1873-5649&rft.volume=218&rft.issue=9&rft.spage=5487&rft.epage=5495&rft_id=info:doi/10.1016%2Fj.amc.2011.11.037&rft.externalDocID=S0096300311013671 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0096-3003&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0096-3003&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0096-3003&client=summon |