Numerical Solutions of Coupled Burgers’ Equations
In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers’ equations. These modifications are made with the help of auxiliary parameters to speed up the convergence rate of the series solutions. Three numerical test problems are...
Uložené v:
| Vydané v: | Axioms Ročník 8; číslo 4; s. 119 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Basel
MDPI AG
2019
|
| Predmet: | |
| ISSN: | 2075-1680, 2075-1680 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers’ equations. These modifications are made with the help of auxiliary parameters to speed up the convergence rate of the series solutions. Three numerical test problems are given to judge the behavior of the modified algorithms, and error norms are used to evaluate the accuracy of the method. Numerical simulations are carried out for different values of parameters. The results are also compared with the existing methods in the literature. |
|---|---|
| AbstractList | In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers’ equations. These modifications are made with the help of auxiliary parameters to speed up the convergence rate of the series solutions. Three numerical test problems are given to judge the behavior of the modified algorithms, and error norms are used to evaluate the accuracy of the method. Numerical simulations are carried out for different values of parameters. The results are also compared with the existing methods in the literature. |
| Author | Ahmad, Hijaz Cesarano, Clemente Khan, Tufail A. |
| Author_xml | – sequence: 1 givenname: Hijaz orcidid: 0000-0002-5438-5407 surname: Ahmad fullname: Ahmad, Hijaz – sequence: 2 givenname: Tufail A. surname: Khan fullname: Khan, Tufail A. – sequence: 3 givenname: Clemente surname: Cesarano fullname: Cesarano, Clemente |
| BookMark | eNp1kMFKAzEQhoNUsNYevS94Xp0ku5vkqKVqoehBPYckm5SUbdMmu6A3X8PX80lcWxEVnMsMM9_8M_zHaLAOa4vQKYZzSgVcqGcfVolDARiLAzQkwMocVxwGP-ojNE5pCX0ITDmmQ0TvupWN3qgmewhN1_qwTllw2SR0m8bW2VUXFzam99e3bLrt1G5-gg6dapIdf-URerqePk5u8_n9zWxyOc8NZdDmxHDuXK1cWQknrKYF01gQ5hStRAWEEqtYXWgoCFfKOGs1NqJUGmrQNQM6QrO9bh3UUm6iX6n4IoPyctcIcSFVbL1prHTaWOIsI3VJirrS2jgAajgTqiJAba91ttfaxLDtbGrlMnRx3b8vSVlUnPECFz2V7ykTQ0rRuu-rGOSnzfKXzT1P__DGtzuT2qh888_WB3R0hRM |
| CitedBy_id | crossref_primary_10_1016_j_apnum_2022_10_014 crossref_primary_10_1007_s13226_021_00031_w crossref_primary_10_1016_j_cjph_2021_10_044 crossref_primary_10_1515_gmj_2021_2135 crossref_primary_10_1371_journal_pone_0304735 crossref_primary_10_1016_j_apnum_2024_06_019 crossref_primary_10_1080_17455030_2021_1876961 crossref_primary_10_1007_s11766_025_5127_7 crossref_primary_10_1108_HFF_01_2020_0029 crossref_primary_10_1155_2022_8613490 crossref_primary_10_1177_14613484241230832 crossref_primary_10_5269_bspm_63270 crossref_primary_10_1007_s11227_025_07141_w crossref_primary_10_1088_1873_7005_ad8d08 crossref_primary_10_1007_s11082_022_03891_6 crossref_primary_10_1002_mma_6614 crossref_primary_10_1002_mma_7527 crossref_primary_10_3390_sym12071195 crossref_primary_10_1007_s11082_022_04186_6 crossref_primary_10_1007_s40065_020_00308_8 crossref_primary_10_1007_s40819_021_00985_9 crossref_primary_10_1002_mma_7161 crossref_primary_10_1108_MMMS_01_2022_0011 crossref_primary_10_12677_AAM_2024_1312503 crossref_primary_10_3390_math11092071 crossref_primary_10_3390_math8060908 crossref_primary_10_1007_s40819_021_01132_0 crossref_primary_10_1016_j_camwa_2021_03_026 crossref_primary_10_1007_s11075_024_01936_3 crossref_primary_10_1155_2021_5549288 crossref_primary_10_1177_14613484231184701 crossref_primary_10_32604_sv_2021_014157 crossref_primary_10_1063_5_0084540 crossref_primary_10_1080_16583655_2020_1741943 |
| Cites_doi | 10.1016/j.cam.2006.07.009 10.1016/j.enganabound.2008.06.005 10.3846/13926292.2014.909897 10.1108/HFF-07-2019-0577 10.1007/s10910-019-01063-8 10.1016/j.aml.2019.01.016 10.1177/1461348418823126 10.34198/ejms.2119.127142 10.34198/ejms.2119.2937 10.1177/1461348418811028 10.1016/j.physa.2013.10.030 10.2478/cmam-2009-0026 10.1016/j.camwa.2006.12.083 10.1016/j.cpc.2013.11.012 10.1016/j.cam.2007.11.007 10.1155/S0161171201010249 10.1016/j.cnsns.2018.09.007 10.1016/j.cnsns.2010.06.028 10.1016/j.camwa.2019.03.053 |
| ContentType | Journal Article |
| Copyright | 2019 by the authors. 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 (http://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: 2019 by the authors. 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 (http://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 PRINS PTHSS Q9U DOA |
| DOI | 10.3390/axioms8040119 |
| 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 ProQuest Central Technology collection ProQuest One Community College ProQuest Central Korea Engineering Research Database ProQuest Central Student SciTech Premium Collection (via ProQuest) ProQuest Computer Science Collection Computer Science Database 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 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 ProQuest Central China 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 China 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 Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2075-1680 |
| ExternalDocumentID | oai_doaj_org_article_fbce2fe72d524d6bbcf003c879a6203e 10_3390_axioms8040119 |
| GroupedDBID | 5VS 8FE 8FG AADQD AAFWJ AAYXX ABDBF ABJCF ABUWG ACUHS ADBBV AFFHD AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS AMVHM ARAPS AZQEC BCNDV BENPR BGLVJ BPHCQ CCPQU CITATION DWQXO EAD EAP ESX GNUQQ GROUPED_DOAJ HCIFZ IAO K6V K7- KQ8 L6V M7S MODMG M~E OK1 PHGZM PHGZT PIMPY PQGLB PQQKQ PROAC PTHSS QF4 QN7 3V. 7SC 7TB 7XB 8AL 8FD 8FK FR3 JQ2 KR7 L7M L~C L~D M0N P62 PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c370t-2c88ffdaf569f9eb347b1927fa36960232ea7d4b0428aacfeeb1c95ab0d0bd703 |
| IEDL.DBID | M7S |
| ISICitedReferencesCount | 54 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000505589700015&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2075-1680 |
| IngestDate | Fri Oct 03 12:42:54 EDT 2025 Fri Jul 25 12:09:04 EDT 2025 Tue Nov 18 22:36:58 EST 2025 Sat Nov 29 07:15:43 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c370t-2c88ffdaf569f9eb347b1927fa36960232ea7d4b0428aacfeeb1c95ab0d0bd703 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-5438-5407 |
| OpenAccessLink | https://www.proquest.com/docview/2546878414?pq-origsite=%requestingapplication% |
| PQID | 2546878414 |
| PQPubID | 2032429 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_fbce2fe72d524d6bbcf003c879a6203e proquest_journals_2546878414 crossref_primary_10_3390_axioms8040119 crossref_citationtrail_10_3390_axioms8040119 |
| PublicationCentury | 2000 |
| PublicationDate | 2019-00-00 |
| PublicationDateYYYYMMDD | 2019-01-01 |
| PublicationDate_xml | – year: 2019 text: 2019-00-00 |
| PublicationDecade | 2010 |
| PublicationPlace | Basel |
| PublicationPlace_xml | – name: Basel |
| PublicationTitle | Axioms |
| PublicationYear | 2019 |
| Publisher | MDPI AG |
| Publisher_xml | – name: MDPI AG |
| References | Islam (ref_2) 2009; 33 Mittal (ref_5) 2011; 16 Lai (ref_6) 2014; 395 Mohammadi (ref_9) 2014; 19 Ahmad (ref_13) 2019; 2 Nadeem (ref_23) 2019; 78 ref_11 He (ref_18) 2007; 207 He (ref_19) 2007; 54 Kaya (ref_4) 2001; 27 Rashid (ref_7) 2014; 245 Yu (ref_16) 2018; 38 Anjum (ref_15) 2019; 92 Ahmad (ref_21) 2018; 9 Rashid (ref_1) 2009; 9 Ahmad (ref_14) 2019; 38 He (ref_17) 2003; 143 He (ref_12) 2010; 1 He (ref_25) 2019; 57 Khater (ref_3) 2008; 222 ref_24 ref_20 Rafiq (ref_22) 2017; 8 Bak (ref_10) 2019; 69 Kumar (ref_8) 2014; 185 |
| References_xml | – volume: 245 start-page: 372 year: 2014 ident: ref_7 article-title: Numerical solution of the coupled viscous Burgers equations by Chebyshev–Legendre Pseudo-Spectral method publication-title: Appl. Math. Comput. – volume: 207 start-page: 3 year: 2007 ident: ref_18 article-title: Variational iteration method—Some recent results and new interpretations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2006.07.009 – volume: 33 start-page: 399 year: 2009 ident: ref_2 article-title: A meshfree interpolation method for the numerical solution of the coupled nonlinear partial differential equations publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2008.06.005 – volume: 19 start-page: 180 year: 2014 ident: ref_9 article-title: A reproducing kernel method for solving a class of nonlinear systems of pdes publication-title: Math. Model. Anal. doi: 10.3846/13926292.2014.909897 – volume: 8 start-page: 389 year: 2017 ident: ref_22 article-title: Variational iteration method with an auxiliary parameter for solving Volterra’s population model publication-title: Nonlinear Sci. Lett. A – ident: ref_24 doi: 10.1108/HFF-07-2019-0577 – ident: ref_11 – volume: 57 start-page: 2075 year: 2019 ident: ref_25 article-title: A variational principle for a thin film equation publication-title: J. Math. Chem. doi: 10.1007/s10910-019-01063-8 – volume: 92 start-page: 134 year: 2019 ident: ref_15 article-title: Laplace transform: Making the variational iteration method easier publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2019.01.016 – volume: 38 start-page: 1113 year: 2019 ident: ref_14 article-title: Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations publication-title: J. Low Freq. Noise Vib. Act. Control doi: 10.1177/1461348418823126 – ident: ref_20 doi: 10.34198/ejms.2119.127142 – volume: 2 start-page: 29 year: 2019 ident: ref_13 article-title: Variational Iteration Algorithm-I with an Auxiliary Parameter for Solving Fokker-Planck Equation publication-title: Earthline J. Math. Sci. doi: 10.34198/ejms.2119.2937 – volume: 38 start-page: 1540 year: 2018 ident: ref_16 article-title: Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators publication-title: J. Low Freq. Noise Vib. Act. Control doi: 10.1177/1461348418811028 – volume: 395 start-page: 445 year: 2014 ident: ref_6 article-title: A new lattice Boltzmann model for solving the coupled viscous Burgers’ equation publication-title: Phys. A: Stat. Mech. Appl. doi: 10.1016/j.physa.2013.10.030 – volume: 9 start-page: 412 year: 2009 ident: ref_1 article-title: A Fourier Pseudospectral Method for Solving Coupled Viscous Burgers Equations publication-title: Comput. Methods Appl. Math. doi: 10.2478/cmam-2009-0026 – volume: 54 start-page: 881 year: 2007 ident: ref_19 article-title: Variational iteration method: New development and applications publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2006.12.083 – volume: 143 start-page: 533 year: 2003 ident: ref_17 article-title: Variational approach to the Thomas–Fermi equation publication-title: Appl. Math. Comput. – volume: 185 start-page: 809 year: 2014 ident: ref_8 article-title: A composite numerical scheme for the numerical simulation of coupled Burgers’ equation publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2013.11.012 – volume: 9 start-page: 27 year: 2018 ident: ref_21 article-title: Variational iteration method with an auxiliary parameter for solving differential equations of the fifth order publication-title: Nonlinear Sci. Lett. A – volume: 222 start-page: 333 year: 2008 ident: ref_3 article-title: A Chebyshev spectral collocation method for solving Burgers’-type equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.11.007 – volume: 1 start-page: 1 year: 2010 ident: ref_12 article-title: The variational iteration method which should be followed publication-title: Nonlinear Sci. Lett. A – volume: 27 start-page: 675 year: 2001 ident: ref_4 article-title: An explicit solution of coupled viscous Burgers′ equation by the decomposition method publication-title: Int. J. Math. Math. Sci. doi: 10.1155/S0161171201010249 – volume: 69 start-page: 31 year: 2019 ident: ref_10 article-title: A semi-Lagrangian approach for numerical simulation of coupled Burgers’ equations publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2018.09.007 – volume: 16 start-page: 1304 year: 2011 ident: ref_5 article-title: Numerical solution of the coupled viscous Burgers’ equation publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2010.06.028 – volume: 78 start-page: 2052 year: 2019 ident: ref_23 article-title: Modified Laplace variational iteration method for solving fourth-order parabolic partial differential equation with variable coefficients publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2019.03.053 |
| SSID | ssj0000913813 |
| Score | 2.358091 |
| Snippet | In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers’ equations. These... In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers' equations. These... |
| SourceID | doaj proquest crossref |
| SourceType | Open Website Aggregation Database Enrichment Source Index Database |
| StartPage | 119 |
| SubjectTerms | Accuracy Algorithms Approximation Burgers equation coupled burgers equation Iterative algorithms Iterative methods Lagrange multiplier modified variational iteration algorithm-i modified variational iteration algorithm-ii mvia-ii Norms Parameter modification Partial differential equations |
| SummonAdditionalLinks | – databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3LSsNAFB1EXOhCfGK1ShbiytDJZDKPpS0tLrS4UOguzBMKtalNKy79DX_PL3Emk4aKiBu34YaEe-5zbnIuAJeGEiFcqosRkTrGIvNDQkOcu-tE-Jrf6ArpOzocstGIP6yt-vLfhAV64KC4jpXKIGso0hnCmkiprDNExSgXBMHU-OgLKV9rpqoYzBOXitJAqpm6vr4j3sbFc8mczSaeVWctCVVc_T9CcZVfBntgty4Mo5vwQvtgw0wPwM59w6paHoJ0uAzzlUnUnGZFhY16xXI2MTrqVr84l5_vH1H_JVB4l0fgadB_7N3G9dKDWKUULmKkGLNWC5sRbrlrdTGVrgqjVvjNey7DIiOoxtL3OkIoa1ywVTwTEmootfPfY7A5LabmBEQYagbdbQKaDBPEmWQktUQLlUrNEtEC1yst5KpmBPeLKSa56wy80vJvSmuBq0Z8FqgwfhPsepU2Qp7BurrgcM1rXPO_cG2B9gqQvHarMvfk_cxPSvHpfzzjDGy7-oeHE5U22FzMl-YcbKnXxbicX1QW9QXhGNPy priority: 102 providerName: Directory of Open Access Journals |
| Title | Numerical Solutions of Coupled Burgers’ Equations |
| URI | https://www.proquest.com/docview/2546878414 https://doaj.org/article/fbce2fe72d524d6bbcf003c879a6203e |
| Volume | 8 |
| WOSCitedRecordID | wos000505589700015&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 Directory of Open Access Journals customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: DOA dateStart: 20120101 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: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: M~E dateStart: 20120101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: K7- dateStart: 20120301 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: M7S dateStart: 20120301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: BENPR dateStart: 20120301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Publicly Available Content Database customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: PIMPY dateStart: 20120301 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9tAEB5R4NAeeLWogRD5UHGqhd-7PiESGYEoVgStRE_WPhFSiEOcVD0h_gZ_j1_Cztpxi1B74bIH71qyd94zu98AfFEkYcyYOjdIuHQjFmORUCVG3KXP0OdX0lL6G8lzenWVDpuEW9Ucq1zoRKuoZSkwR36AuO0Ui2TR4eTOxa5RWF1tWmi8gxVESfDt0b3LNseCmJfUD2tozdBE9wfs9015W1HDuT5i6_xliixi_yuFbK3M8fpbv28D1hr_0jmqGWITltR4Cz6ct-Cs1UcI83ldphk5bVLMKbUzKOeTkZJO396Urp4eHp3srkYCrz7Bj-Ps--DEbXonuCIk3swNBKVaS6bjJNWpiZgjwo0zRzTDBn7GUAeKERlxDJkYE1oZnS3SmHFPelwaNbANy-NyrD6DE3mSeuY15inzj0FKOU1CnUgmQi6pzzrwdbGNhWiAxbG_xagwAQbuevFi1zuw3y6f1Iga_1rYR5q0ixAI2z4op9dFI1eF5kIFWpFAxkEkE86FNnpKUJKyJPBC1YHuglxFI51V8YdWO_-f3oX3xkFK65RLF5Zn07nag1Xxa3ZTTXuw0s_y4UXPxvFmPCNuzzIgjveZmR-eng9_PgMy7ec0 |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3LTttAFL2iFKllQSkFkfLyonSFhTPjeMYLhHgKlBCxoBI7d54IKY1DnLRlx2_wE3wUX8Jcv1qEYMeCrT22rLnnvj3nAnwzLBLCuTqfRFL7oWhhk9BETt11U2DMb3Qu6Q7rdvn5eXw6AXfVWRj8rbKyibmh1qnCGvkm8rZzbJKF24MrH6dGYXe1GqFRwKJtrv-4lC3bOt538l0n5PDgbO_IL6cK-IqyYOQTxbm1WthWFNvY5ZIhky7MYVbgaDvnwogRTIcSkwkhlDXOmqm4JWSgA6mdgrj3voP3IeUM9arN_LqmgxybvEkLKk9K42BT_L1Mf2XcaUoTuXz-c335hIAnDiD3aoef3tp-zMJMGT97OwXgP8OE6c_B9ElNPpt9AdodF22onlcX_bzUenvpeNAz2tvNT4Jn9ze33sFVwXSezcOPV_nqBZjsp32zCF4YaB64x0Rg3J6SmEseURtpoajUvCkasFGJLVElcTrO7-glLoFCKSePpNyA7_XyQcEY8tzCXcRAvQiJvvML6fAiKe1GYqUyxBpGdIuEOpJSWWeHFWexiEhATQOWK3gkpfXJkn_Y-Pry7TX4cHR20kk6x932Enx0wWBclJeWYXI0HJsVmFK_R5fZcDUHugc_XxtJD2mBQBc |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3LTttAFL2ioapgAbQFEaCtF21XtWKPX-MFQgUSNYJYWbQSXbnzREghDnHCY8dv8Cv9nH4Jd_wqVdXuWLC1x5ble-575lyA9yoKGUNXZ5OQS9tngWkSqhDVXbrMxPxKFpI-jpKEnpzEwwX4WZ-FMdsqa5tYGGqZCVMj7xjedmqaZH5HV9sihoe9vcmFbSZImU5rPU6jhMiRurnC9C3f7R-irD8Q0ut-PfhiVxMGbOFFzswmglKtJdNBGOsY80o_4hjyRJqZMXfozohikfS5SSwYE1qhZRNxwLgjHS5RWfC9z2ARQ3KftGBx2B8MvzcVHsO4SV2vJPb0vNjpsOuz7DynqDeuYfZ54AiLeQF_uYPCx_VWn_LfWYOVKrK2Ppeq8BIW1PgVLA8aWtr8NXjJvGxQjaymHGhl2jrI5pORktZ-cUY8_3V7Z3UvSg70fB2-PcpXb0BrnI3VJli-I6mDjzFH4f8lMeU09HQomfC4pC5rw6dahKmoKNXNZI9RiqmVkXj6h8Tb8LFZPim5RP61cN_goVlkKMCLC9n0NK0sSqq5UESriMiA-DLkXGi00IJGMQuJ46k27NRQSSu7lKe_cbL1_9vv4AUCKD3uJ0fbsIRRYlzWnXagNZvO1Rt4Li5nZ_n0bYV6C348NpTuAUEBSpg |
| 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+Solutions+of+Coupled+Burgers%E2%80%99+Equations&rft.jtitle=Axioms&rft.au=Hijaz+Ahmad&rft.au=Khan%2C+Tufail+A&rft.au=Cesarano%2C+Clemente&rft.date=2019&rft.pub=MDPI+AG&rft.eissn=2075-1680&rft.volume=8&rft.issue=4&rft.spage=119&rft_id=info:doi/10.3390%2Faxioms8040119&rft.externalDBID=HAS_PDF_LINK |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2075-1680&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2075-1680&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2075-1680&client=summon |