Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations
In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to f...
Saved in:
| Published in | Journal of Mathematics Vol. 2021; pp. 1 - 15 |
|---|---|
| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo
Hindawi
04.06.2021
Hindawi Limited John Wiley & Sons, Inc Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2314-4629 2314-4785 |
| DOI | 10.1155/2021/6636607 |
Cover
| Abstract | In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to finite difference and hybrid difference methods. An error estimate is derived with the discrete norm. In the end, numerical examples are given to show the advantages of the proposed results (Mathematics Subject Classification: 65L11, 65L12, and 65L20). |
|---|---|
| AbstractList | In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to finite difference and hybrid difference methods. An error estimate is derived with the discrete norm. In the end, numerical examples are given to show the advantages of the proposed results (Mathematics Subject Classification: 65L11, 65L12, and 65L20). |
| Author | Vadivel, R. Tamilselvan, A. Agarwal, Praveen Sekar, E. Hammachukiattikul, P. Gunasekaran, N. |
| Author_xml | – sequence: 1 givenname: P. orcidid: 0000-0003-0267-110X surname: Hammachukiattikul fullname: Hammachukiattikul, P. organization: Department of MathematicsPhuket Rajabhat University83000 PhuketThailandpkru.ac.th – sequence: 2 givenname: E. orcidid: 0000-0003-2580-0787 surname: Sekar fullname: Sekar, E. organization: Department of MathematicsSASTRA Deemed to be UniversityThanjavurTamilnadu 613401India – sequence: 3 givenname: A. orcidid: 0000-0002-3440-9352 surname: Tamilselvan fullname: Tamilselvan, A. organization: Department of MathematicsBharathidasan UniversityTiruchirappalli-620 024TamilnaduIndiabdu.ac.in – sequence: 4 givenname: R. orcidid: 0000-0002-1385-5345 surname: Vadivel fullname: Vadivel, R. organization: Department of MathematicsPhuket Rajabhat University83000 PhuketThailandpkru.ac.th – sequence: 5 givenname: N. orcidid: 0000-0003-0375-7917 surname: Gunasekaran fullname: Gunasekaran, N. organization: Department of Mathematical SciencesShibaura Institute of TechnologySaitama 337-8570Japanshibaura-it.ac.jp – sequence: 6 givenname: Praveen orcidid: 0000-0001-7556-8942 surname: Agarwal fullname: Agarwal, Praveen organization: Department of MathematicsAnand International College of EngineeringJaipurIndiaanandice.ac.in |
| BackLink | https://cir.nii.ac.jp/crid/1874242817604439296$$DView record in CiNii |
| BookMark | eNp9kU1P3DAQhqOKSqWUW39ApPZWUuzxR-IjWmiLRD8k2rM1sR3wKmsvjkO1_75eAhekcrEt63mfGXveVgchBldV7yn5TKkQp0CAnkrJpCTtq-oQGOUNbztx8HSWoN5Ux9O0JoRQ6FinyGHlVnGzxYTZ37v6Os92V8dQ_5g3LnmDY_3d5dtop3qIqb724WYeMY27-pdLeU69s_WZvcdgnG3O3Yi7-twPg0suZF_CF3dzEccwvateDzhO7vhxP6r-fLn4vfrWXP38erk6u2oMV11uem4E74VknVMKCDMEsHcUDBWkA5ACiVMULEcHTPTWtNAqlC2nPUfsenZUXS5eG3Gtt8lvMO10RK8fLmK60ZiyN6PTCqB8QpEiK-GBIQEytEwqtKWyUsX1YXFtU7yb3ZT1Os4plPY1CE44aZnYU7BQJsVpSm7QxueHR-eEftSU6P109H46-nE6JXTyLPTU6n_wjwsevC_6_Uq7lgOHjraScM4UKFmwTwt264PFv_5l6T-L3Kb9 |
| CitedBy_id | crossref_primary_10_1080_00207160_2024_2312891 crossref_primary_10_1155_2024_3772081 crossref_primary_10_1016_j_comcom_2023_04_008 crossref_primary_10_1142_S0219265921460051 crossref_primary_10_3390_electronics12081801 crossref_primary_10_1016_j_apnum_2024_09_001 crossref_primary_10_1007_s40819_022_01367_5 crossref_primary_10_1155_2023_3025513 crossref_primary_10_3390_fractalfract7010043 crossref_primary_10_1007_s40819_021_01135_x crossref_primary_10_1016_j_apnum_2022_08_008 crossref_primary_10_1155_2022_2466367 |
| Cites_doi | 10.1016/s0006-3495(65)86709-1 10.1016/j.cam.2020.113050 10.1016/s0006-3495(67)86574-3 10.1023/a:1019681130824 10.1007/bf00275686 10.1007/bf01047829 10.1002/nme.1555 10.1080/00207160310001606052 10.1007/s12190-018-1198-4 10.1016/j.apnum.2020.02.021 10.1142/2933 10.1016/j.apnum.2005.08.002 10.1137/s0036139992228119 10.1137/0142036 10.1137/S0036139992228120 10.1590/s0101-82052005000200001 10.3390/sym12111850 10.1016/j.cam.2017.11.017 10.1016/j.cam.2015.09.003 10.1137/040603425 10.1007/bf01047828 10.1515/cmam-2012-0001 10.1016/j.amc.2008.05.140 10.1016/j.jmaa.2005.02.014 |
| ContentType | Journal Article |
| Copyright | Copyright © 2021 P. Hammachukiattikul et al. Copyright © 2021 P. Hammachukiattikul et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
| Copyright_xml | – notice: Copyright © 2021 P. Hammachukiattikul et al. – notice: Copyright © 2021 P. Hammachukiattikul et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
| DBID | RHU RHW RHX RYH 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 | 10.1155/2021/6636607 |
| DatabaseName | Hindawi Publishing Complete Hindawi Publishing Subscription Journals Hindawi Publishing Open Access CiNii Complete 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 & Aerospace Collection ProQuest Central Essentials ProQuest Central Technology Collection ProQuest One Community College ProQuest Central Engineering Research Database ProQuest Central Student SciTech Premium Collection 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 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: RHX name: Hindawi Publishing Open Access url: http://www.hindawi.com/journals/ sourceTypes: Publisher – sequence: 2 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 3 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2314-4785 |
| Editor | Qin, Xiaolong |
| Editor_xml | – sequence: 1 givenname: Xiaolong surname: Qin fullname: Qin, Xiaolong |
| EndPage | 15 |
| ExternalDocumentID | oai_doaj_org_article_922128226a3b4af3a020f7369ad20399 10_1155_2021_6636607 |
| GroupedDBID | 3V. 4.4 5VS 8FE 8FG AAFWJ AAJEY ABJCF ABUWG ACIPV ACIWK ADBBV AFKRA AFPKN ALMA_UNASSIGNED_HOLDINGS ARAPS AZQEC BCNDV BENPR BGLVJ BPHCQ CCPQU DWQXO EBS ESX GNUQQ GROUPED_DOAJ HCIFZ IAO IHR K6V K7- KQ8 L6V M0N M7S OK1 PIMPY PQQKQ PROAC PTHSS RHU RHW RHX 0R~ 24P ACCMX H13 ITC PHGZM PHGZT RYH AAYXX CITATION 7SC 7TB 7XB 8AL 8FD 8FK AAMMB AEFGJ AGXDD AIDQK AIDYY FR3 JQ2 KR7 L7M L~C L~D P62 PKEHL PQEST PQGLB PQUKI PRINS Q9U PUEGO |
| ID | FETCH-LOGICAL-c498t-b4c54b5638e99203c02abe12c15082265a0e912d4ae235bdc7279a6741b4aa8b3 |
| IEDL.DBID | RHX |
| ISSN | 2314-4629 |
| IngestDate | Wed Aug 27 01:27:19 EDT 2025 Fri Jul 25 12:06:08 EDT 2025 Tue Jul 01 04:01:29 EDT 2025 Thu Apr 24 23:05:55 EDT 2025 Fri Jun 27 00:05:19 EDT 2025 Sun Jun 02 19:16:05 EDT 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| License | This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. https://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c498t-b4c54b5638e99203c02abe12c15082265a0e912d4ae235bdc7279a6741b4aa8b3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-3440-9352 0000-0001-7556-8942 0000-0002-1385-5345 0000-0003-0375-7917 0000-0003-0267-110X 0000-0003-2580-0787 0009-0001-8725-2109 0000-0003-0267-110x |
| OpenAccessLink | https://dx.doi.org/10.1155/2021/6636607 |
| PQID | 2540407359 |
| PQPubID | 2037347 |
| PageCount | 15 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_922128226a3b4af3a020f7369ad20399 proquest_journals_2540407359 crossref_citationtrail_10_1155_2021_6636607 crossref_primary_10_1155_2021_6636607 nii_cinii_1874242817604439296 hindawi_primary_10_1155_2021_6636607 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2021-06-04 |
| PublicationDateYYYYMMDD | 2021-06-04 |
| PublicationDate_xml | – month: 06 year: 2021 text: 2021-06-04 day: 04 |
| PublicationDecade | 2020 |
| PublicationPlace | Cairo |
| PublicationPlace_xml | – name: Cairo |
| PublicationTitle | Journal of Mathematics |
| PublicationYear | 2021 |
| Publisher | Hindawi Hindawi Limited John Wiley & Sons, Inc Wiley |
| Publisher_xml | – name: Hindawi – name: Hindawi Limited – name: John Wiley & Sons, Inc – name: Wiley |
| References | 23 24 25 27 28 P. Selvi (26) 2016; 296 J. Miller (29) 1996 A. Rahmoune (8) 2020; 1 C. Lange (11) 1994; 54 30 M. Abbas (9) 2020; 48 12 13 14 15 17 Y. Kuang (5) 1993 18 19 V. Subburayan (22) 2013; 43 1 2 M. Kadalbajoo (16) 2006; 23 3 4 6 7 M. Timoumi (10) 2019; 3 20 21 |
| References_xml | – ident: 6 doi: 10.1016/s0006-3495(65)86709-1 – ident: 24 doi: 10.1016/j.cam.2020.113050 – ident: 7 doi: 10.1016/s0006-3495(67)86574-3 – ident: 18 doi: 10.1023/a:1019681130824 – ident: 2 doi: 10.1007/bf00275686 – ident: 3 doi: 10.1007/bf01047829 – ident: 19 doi: 10.1002/nme.1555 – ident: 20 doi: 10.1080/00207160310001606052 – ident: 23 doi: 10.1007/s12190-018-1198-4 – ident: 25 doi: 10.1016/j.apnum.2020.02.021 – volume-title: Fitted Numerical Methods for Singular Perturbation Problems year: 1996 ident: 29 doi: 10.1142/2933 – volume: 3 issue: 305–316 year: 2019 ident: 10 article-title: Infinitely many homoclinic solutions for fourth-order differential equations with locally defined potentials publication-title: Journal of Nonlinear and Variational Analysis – volume: 1 start-page: 1 year: 2020 ident: 8 article-title: Growth of solutions for a coupled nonlinear klein–gordon system with strong damping, source, and distributed delay terms publication-title: Advances in Difference Equations – ident: 30 doi: 10.1016/j.apnum.2005.08.002 – ident: 12 doi: 10.1137/s0036139992228119 – ident: 13 doi: 10.1137/0142036 – volume: 23 start-page: 180 year: 2006 ident: 16 article-title: Parameter-uniform fitted mesh method for singularly perturbed delay differential equations with layer behavior publication-title: Electronic Transactions on Numerical Analysis – volume: 54 start-page: 249 year: 1994 ident: 11 article-title: Singular perturbation analysis of boundary-value problems for differential-difference equations (v) small shifts with layer behavior publication-title: SIAM Journal of Applied Mathematics doi: 10.1137/S0036139992228120 – volume-title: Delay Differential Equations with Applications in Population Dynamics year: 1993 ident: 5 – ident: 14 doi: 10.1590/s0101-82052005000200001 – ident: 28 doi: 10.3390/sym12111850 – ident: 15 doi: 10.1016/j.cam.2017.11.017 – volume: 296 start-page: 10 year: 2016 ident: 26 article-title: An iterative numerical method for singularly perturbed reaction–diffusion equations with negative shift publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2015.09.003 – ident: 4 doi: 10.1137/040603425 – ident: 1 doi: 10.1007/bf01047828 – ident: 27 doi: 10.1515/cmam-2012-0001 – ident: 17 doi: 10.1016/j.amc.2008.05.140 – volume: 43 start-page: 67 issue: 2 year: 2013 ident: 22 article-title: An initial value technique for singularly perturbed reaction-diffusion problems with a negative shift publication-title: Novi Sad Journal of Mathematics – volume: 48 year: 2020 ident: 9 article-title: Existence results and the ulam stability for fractional differential equations with hybrid proportional-caputo derivatives publication-title: Journal Nonlinear Functional Analysis ID – ident: 21 doi: 10.1016/j.jmaa.2005.02.014 |
| SSID | ssj0001283890 ssib026596782 ssib050733809 |
| Score | 2.2327013 |
| Snippet | In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid... |
| SourceID | doaj proquest crossref nii hindawi |
| SourceType | Open Website Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1 |
| SubjectTerms | Comparative studies Decomposition Differential equations Finite difference method Mathematical analysis Mathematics Methods Numerical analysis Numerical methods QA1-939 |
| SummonAdditionalLinks | – databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8QwEA7iSQ_iE9cXOehJgm2apM3RJyKsCCp4K3ktLpSquyuy_96ZNLssiHjx0sMS2DCZzvdNO_0-Qo4LaZ2Hbod57jUT1npmeeDMOOmk9abKJX6N3L9Xt8_i7kW-LFh94UxYJw_cBe5McyiugGLKFFaYQWGA3wzKQmnjeQboitU309lCMwWZJNGKcCZM1T1tqQCZs-g0lwsmFNezKXgp8QFAfgbQqxS6yi7gU5TxB2b8iv3x1xDwpx0Of1TtCEU362QtcUh63u19gyyFdpOs9ucCrOMtEt0akqo3xVnBKX1r6f1n936mof1oHD2mQFnpI6AXDqM2U_oQRgBBNnh6nmYD2FVozJReJR8VqAcNvf7o9MHH2-T55vrp8pYlRwXmhK4mzAonhZVwzwWtIXwu48aGnDtUhYcYS5MFnXMvTOBwit4Bu9FGAeuA2JvKFjtkuX1rwy6hygxcaXShgkUJfleFANwulJkJVjnBe-R0FsfaJblxdL1o6th2SFlj1OsU9R45ma9-72Q2fll3gUcyX4Pi2PEHSJk6pUz9V8r0yHE60D_-6xBOGzaPV7QuBDZT5aXKhEBSqXrkYJYHdbrxxzX021AWy0Lqvf_Y6j5ZwS3F2TRxQJYno89wCCxoYo9iwn8DXIj5cg priority: 102 providerName: Directory of Open Access Journals – databaseName: ProQuest Central dbid: BENPR link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwhV1NT9wwELUoXNoDaqFVlwLygZ4qi8SxnfhUQVmEKu0KtUXiFvlr25WiLGwWof33nXGcpVJFe8khseTEM555tifvEXJSSOs8rHaY514zYa1nlgfOjJNOWm-qXOLfyJOpuroRX2_lbdpw61JZ5RATY6D2C4d75KewkAF_KwupP9_dM1SNwtPVJKHxguxACK7Az3fOx9Prb4NHSZQkHAiq-l2XCjJ0FhXncsGE4nqohpcSNwLyU0jBSqG67B95KtL5A0L-hevkxznkoXY-_yt6x5R0-ZrsJixJz3rjvyFbod0jryYbItZun0TVhsTuTbFmcE0XLZ0-9Oc0DZ1EAemOAnSl3yGLYVFqs6bXYQmpyAZPz1KNALsIjVnTi6SnAnGhoeP7nie8e0tuLsc_vlyxpKzAnNDVilnhpLAS5l7QmmeFy7ixIecO2eEBkEmTBZ1zL0zgYE3vAOVoowB9WGFMZYt3ZLtdtOE9ocrMXGl0oYJFKn5XhQAYL5SZCVY5wUfk0zCOtUu046h-0dRx-SFljaNep1EfkY-b1nc93cYz7c7RJJs2SJIdbyyWP-s052rN0Sngc0wBrz0rDEDjWVkobTx8s9YjcpIM-p--jsDa8PJ4RQlDQDVVXqpMCASXakQOBz-oUwDo6id3Pfj34w_kJXYWq8_EIdleLR_CEeCclT1Ozvwbp0jz0g priority: 102 providerName: ProQuest |
| Title | Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations |
| URI | https://dx.doi.org/10.1155/2021/6636607 https://cir.nii.ac.jp/crid/1874242817604439296 https://www.proquest.com/docview/2540407359 https://doaj.org/article/922128226a3b4af3a020f7369ad20399 |
| Volume | 2021 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1Na9wwEBVtemkPoekH3TRZdEhPRdSWJdk6Js1ul8IuIW1gb0ZfSxeM08Ybwv77zMjy0jaU5mKwEZasGem9scdvCDkppHUeoh3muddMWOuZ5YEz46ST1psql_g38nyhZlfi61Iuk0hS9_ATPqAdhuf5JwBGpfCv8aeVQue9nC0Ht-FKavWbKLvEOoSDKlX_qqUCWM5imblcMKG4HlLg_7r9H-AUNfyBFv_A4PhuDeDTrtcPtuyIQ9OXZD8RSHraW_yAPAntK_JivlNf7V6TWKohSXpTTBTc0uuWLm77jzMNnceq0R0Fvkq_AXRhJmqzpRfhBvDHBk9PU2IAOw-N2dLzVEQFNoOGTn714uDdG3I1nXz_PGOpnAJzQlcbZoWTwkpYcEFrnhUu48aGnDuUhAcWJk0WdM69MIGDCb0DaqONAsphhTGVLd6Svfa6De8IVWblSqMLFSzq77sqBCB2ocxMsMoJPiIfh3msXdIax5IXTR1jDilrnPU6zfqIfNi1_tlrbPyj3RmaZNcGlbHjBfCWOi20WnMAY3wcU8CwV4UBPrwqC6WNh2fWekROkkH_09cxWBsGj0esWwhUpspLlQmBjFKNyNHgB3Va9V0NwTbsiWUh9eHjenlPnuNpTD0TR2Rvc3MbjoHkbOwYHH36ZUyenU0WF5fj-KpgHN3-Hk_v71M |
| linkProvider | Hindawi Publishing |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3LbtNAFB2VsgAWiKcaaMss2hWyas8rngVCpWlIaRMh0UrdmXkFIllOG6eq8lN8I_fa44CEgFU3WSSj2DNzZ8654-tzCNnj0joP2U7imdeJsNYnlgWWGCedtN7kmcS3kccTNboQny7l5Qb50b0Lg2WV3Z7YbNR-7vCM_AASGYi3Ppf6_dV1gq5R-HS1s9Bow-I0rG4hZavfnQxgfvcZGx6fH42S6CqQOKHzZWKFk8JKiLugNUu5S5mxIWMOldGBjEiTBp0xL0xg0BPvAOG1UYC8VhiTWw7_e4_cF5xrtIrIhx-7-JVogNjJYbVnPDnwgbTxt8tEIhTTXe29lHjskB0A4CuFXra_oWJjHgB8_Dtm5bczQL1qNvsDKxoAHD4hjyNzpYdtqD0lG6F6Rh6N17Kv9XPSeERELXGKFYorOq_o5KZ9KlTScWNXXVMgyvQLYCaWwJYr-jksAPhs8PQwViQkg1CaFR1E9xbYhUp6fN2qktcvyMWdjPhLslnNq7BFqDJT1zeaq2BR-N_lIQCjDP3UBKucYD3ythvHwkWRc_TaKIsm2ZGywFEv4qj3yP669VUr7vGXdh9wStZtUJK7-WK--FbEFV5oBiwAu2M43PaUGyDi0z5X2njos9Y9shcn9D_X2oHZhpvHTzRMBA6VZ32VCoFUVvXIdhcHRdxu6uLX4nj175_fkAej8_FZcXYyOX1NHuKFm7o3sU02l4ubsAMMa2l3m7Cm5Otdr6OfPq0uOw |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEF6VVEJwQDxFoIU9tCdkxV7vrr0HhFqSqKUkioBKvZl9BSJZThunqvLX-HXM2OuAhIBTLz7YK-9rdr9v1uP5CDlIhbEOvJ3IMaciboyLDPMs0lZYYZzOE4F_I0-m8uScf7gQFzvkR_cvDIZVdntis1G7pcUz8gE4MmBvWSrUYB7CImbD8bvLqwgVpPBLayen0ZrImd_cgPtWvz0dwlwfMjYefXl_EgWFgchyla8jw63gRoANeqVYnNqYaeMTZjFLOhAToWOvEua49gx65SygvdISUNhwrXOTwnvvkN0MUJH3yO7xaDr71FmzQDnELjlWe-KTAzuIG7W7hEdcMtVF4guBhxDJAOBfSlS2_Q0jGykBYOff0Ue_WQAGVovFH8jRwOH4IXkQeCw9ag3vEdnx1WNyf7JNAls_IY1iRMgsTjFecUOXFZ1et9-ISjppxKtrCrSZfgYExYDYckNnfgUwaLyjRyE-IRr6Um_oMGi5wJ5U0tFVm6O8fkrOb2XMn5Fetaz8c0KlnttMq1R6gzIANvce-KXPYu2NtJz1yZtuHAsbUp6j8kZZNK6PEAWOehFGvU8Ot6Uv21Qffyl3jFOyLYMJupsby9W3Iqz3QjHgBNgdnUKz56kGWj7PUqm0gz4r1ScHYUL_U9c-zDY0Hq8onwiMKk8yGXOOxFb2yV5nB0XYfOri11J58e_Hr8ldWEPFx9Pp2UtyD-ttguD4HumtV9d-H-jW2rwKdk3J19teSj8BEhsz1g |
| 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=Comparative+Study+on+Numerical+Methods+for+Singularly+Perturbed+Advanced-Delay+Differential+Equations&rft.jtitle=Journal+of+mathematics+%28Hidawi%29&rft.au=Hammachukiattikul%2C+P.&rft.au=Sekar%2C+E.&rft.au=Tamilselvan%2C+A.&rft.au=Vadivel%2C+R.&rft.date=2021-06-04&rft.pub=Hindawi&rft.issn=2314-4629&rft.eissn=2314-4785&rft.volume=2021&rft_id=info:doi/10.1155%2F2021%2F6636607&rft.externalDocID=10_1155_2021_6636607 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2314-4629&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2314-4629&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2314-4629&client=summon |