Numerical Scheme for Singularly Perturbed Mixed Delay Differential Equation on Shishkin Type Meshes

Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article. The second-order derivative is multiplied by a small parameter which gives rise to boundary layers at x=0 and x=3 and strong interior la...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Fractal and fractional Ročník 7; číslo 1; s. 43
Hlavní autoři: Elango, Sekar, Unyong, Bundit
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.01.2023
Témata:
Analysis
Bakhvalov–Shishkin mesh
Boundary conditions
Boundary layer
Boundary layers
Boundary value problems
Convergence
Decomposition
Delay
Differential equations
Finite difference method
finite difference scheme
fractional calculus
mixed-delay differential equations
Ordinary differential equations
Shishkin mesh
singular perturbation problems
ISSN:2504-3110, 2504-3110
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article. The second-order derivative is multiplied by a small parameter which gives rise to boundary layers at x=0 and x=3 and strong interior layers at x=1 and x=2 due to the delay terms. We prove that this method is almost first-order convergent on Shishkin mesh and is first-order convergent on Bakhvalov–Shishkin mesh. Error estimates are derived in the discrete maximum norm. Some examples are provided to validate the theoretical result.
AbstractList Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article. The second-order derivative is multiplied by a small parameter which gives rise to boundary layers at x=0 and x=3 and strong interior layers at x=1 and x=2 due to the delay terms. We prove that this method is almost first-order convergent on Shishkin mesh and is first-order convergent on Bakhvalov–Shishkin mesh. Error estimates are derived in the discrete maximum norm. Some examples are provided to validate the theoretical result.
Audience Academic
Author Elango, Sekar
Unyong, Bundit
Author_xml – sequence: 1
  givenname: Sekar
  surname: Elango
  fullname: Elango, Sekar
– sequence: 2
  givenname: Bundit
  surname: Unyong
  fullname: Unyong, Bundit
BookMark eNp9kV9rHCEUxaWk0DTNJ-iL0OdN_TOzjo8hSdtA0gQ2eRZH7911Oztu1IHst6_ZDaGUUhSvXO7vePB8JEdjHIGQz5ydSanZV0zWFTvsi2KcsUa-I8eiZc1Mcs6O_rh_IKc5rxljQmnZMnVM3M9pAyk4O9CFW8EGKMZEF2FcToNNw47eQypT6sHT2_Bcz0sY7I5eBkRIMJZQwaunyZYQR1r3YhXy6lcY6cNuC_QW8gryJ_Ie7ZDh9LWekMdvVw8XP2Y3d9-vL85vZq4Rqsxa7DmDeasBQUqJjDdqroB3KLWTGkGIXne-QYuoOfegvLJCCKs7wa338oRcH3R9tGuzTWFj085EG8y-EdPS2FSCG8Cw1jboAT3O-6brpdaq6VqNc-lrQ0HV-nLQ2qb4NEEuZh2nNFb7RlRXgnVC8Tp1dpha2ioaRoylplCXh01wNSYMtX-uWsF5KztVAXkAXIo5J8A3m5yZlzTNP9KslP6LcqHsv7w-F4b_sr8BpWeryA
CitedBy_id crossref_primary_10_1186_s13661_025_02000_2
crossref_primary_10_33889_IJMEMS_2025_10_5_068
Cites_doi 10.1016/S0006-3495(67)86574-3
10.1007/BF01047829
10.1007/BF01047828
10.1137/0145041
10.1137/0142036
10.1186/s13662-021-03296-x
10.1017/CBO9780511801181
10.1142/2933
10.1023/A:1019681130824
10.1007/BF00275686
10.1137/0145042
10.1016/S0006-3495(65)86709-1
10.1137/040603425
10.1137/S0036139992228120
10.1007/s40819-019-0675-2
10.1016/j.jmaa.2005.02.014
10.1002/nme.1555
10.1007/s12190-018-1198-4
10.1080/00207160310001606052
10.1155/2021/6636607
10.1137/S0036139992228119
ContentType Journal Article
Copyright COPYRIGHT 2022 MDPI AG
2022 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 (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 2022 MDPI AG
– notice: 2022 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 (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
8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
DOA
DOI 10.3390/fractalfract7010043
DatabaseName CrossRef
ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central
SciTech Premium Collection
ProQuest Engineering Collection
Engineering Database
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
ProQuest Central China
Engineering Collection
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
Engineering Collection
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 2504-3110
ExternalDocumentID oai_doaj_org_article_05a4fdefdf6b48b39974859f63d6b47e
A752115387
10_3390_fractalfract7010043
GroupedDBID 8FE
8FG
AADQD
AAFWJ
AAYXX
ABJCF
ADBBV
AFFHD
AFKRA
AFPKN
AFZYC
ALMA_UNASSIGNED_HOLDINGS
BCNDV
BENPR
BGLVJ
CCPQU
CITATION
GROUPED_DOAJ
HCIFZ
IAO
IGS
ITC
L6V
M7S
MODMG
M~E
OK1
PHGZM
PHGZT
PIMPY
PQGLB
PROAC
PTHSS
ABUWG
AZQEC
DWQXO
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
ID FETCH-LOGICAL-c427t-5fb10e659efe333f014767e18f39c39fe22b98d4faff911de7d7a222a9821add3
IEDL.DBID M7S
ISICitedReferencesCount 7
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000919612600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2504-3110
IngestDate Mon Nov 10 04:35:40 EST 2025
Fri Jul 25 11:54:21 EDT 2025
Tue Nov 04 17:52:26 EST 2025
Tue Nov 18 22:28:03 EST 2025
Sat Nov 29 07:16:12 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c427t-5fb10e659efe333f014767e18f39c39fe22b98d4faff911de7d7a222a9821add3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
OpenAccessLink https://www.proquest.com/docview/2767208271?pq-origsite=%requestingapplication%
PQID 2767208271
PQPubID 2055410
ParticipantIDs doaj_primary_oai_doaj_org_article_05a4fdefdf6b48b39974859f63d6b47e
proquest_journals_2767208271
gale_infotracacademiconefile_A752115387
crossref_primary_10_3390_fractalfract7010043
crossref_citationtrail_10_3390_fractalfract7010043
PublicationCentury 2000
PublicationDate 2023-01-01
PublicationDateYYYYMMDD 2023-01-01
PublicationDate_xml – month: 01
  year: 2023
  text: 2023-01-01
  day: 01
PublicationDecade 2020
PublicationPlace Basel
PublicationPlace_xml – name: Basel
PublicationTitle Fractal and fractional
PublicationYear 2023
Publisher MDPI AG
Publisher_xml – name: MDPI AG
References Stein (ref_9) 1967; 7
Rustichini (ref_1) 1989; 1
Kadalbajoo (ref_19) 2004; 81
Patidar (ref_20) 2006; 66
Lange (ref_14) 1982; 42
Abell (ref_3) 2005; 4
ref_12
Lange (ref_15) 1985; 45
ref_23
Chi (ref_4) 1986; 24
ref_22
Kadalbajoo (ref_18) 2005; 307
Sekar (ref_11) 2018; 59
Lange (ref_16) 1985; 45
Govindarao (ref_10) 2022; 2022
Hammachukiattikul (ref_21) 2021; 2021
Rustichini (ref_2) 1989; 1
Lange (ref_6) 1994; 54
ref_5
Stein (ref_8) 1965; 5
Lange (ref_7) 1994; 54
Kadalbajoo (ref_17) 2002; 115
Sekar (ref_13) 2019; 5
References_xml – volume: 7
  start-page: 37
  year: 1967
  ident: ref_9
  article-title: Some models of neuronal variability
  publication-title: Biophys. J.
  doi: 10.1016/S0006-3495(67)86574-3
– volume: 1
  start-page: 145
  year: 1989
  ident: ref_2
  article-title: Hopf bifurcation for functional differential equations of mixed type
  publication-title: J. Dyn. Differ. Equ.
  doi: 10.1007/BF01047829
– volume: 1
  start-page: 121
  year: 1989
  ident: ref_1
  article-title: Functional differential equations of mixed type: The linear autonomous case
  publication-title: J. Dyn. Differ. Equ.
  doi: 10.1007/BF01047828
– ident: ref_5
– volume: 45
  start-page: 687
  year: 1985
  ident: ref_15
  article-title: Singular-Perturbation Analysis of Boundary-Value Problems for Differential-Difference Equations II. Rapid Oscillations and Resonances
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/0145041
– volume: 42
  start-page: 502
  year: 1982
  ident: ref_14
  article-title: Singularly perturbation analysis of boundary-value problems for differential-difference equations
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/0142036
– ident: ref_12
  doi: 10.1186/s13662-021-03296-x
– ident: ref_22
  doi: 10.1017/CBO9780511801181
– ident: ref_23
  doi: 10.1142/2933
– volume: 115
  start-page: 145
  year: 2002
  ident: ref_17
  article-title: Numerical Analysis of Boundary-Value Problems for Singularly-Perturbed Differential-Difference Equations with Small Shifts of Mixed Type
  publication-title: J. Optim. Theory Appl.
  doi: 10.1023/A:1019681130824
– volume: 24
  start-page: 583
  year: 1986
  ident: ref_4
  article-title: Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory
  publication-title: J. Math. Biol.
  doi: 10.1007/BF00275686
– volume: 45
  start-page: 708
  year: 1985
  ident: ref_16
  article-title: Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations III. Turning Point Problems
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/0145042
– volume: 5
  start-page: 173
  year: 1965
  ident: ref_8
  article-title: A Theoretical Analysis of Neuronal Variability
  publication-title: Biophys. J.
  doi: 10.1016/S0006-3495(65)86709-1
– volume: 4
  start-page: 755
  year: 2005
  ident: ref_3
  article-title: Computation of mixed type functional differential boundary value problems
  publication-title: SIAM J. Appl. Dyn. Syst.
  doi: 10.1137/040603425
– volume: 54
  start-page: 249
  year: 1994
  ident: ref_6
  article-title: Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations. V. Small Shifts with Layer Behavior
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/S0036139992228120
– volume: 5
  start-page: 85
  year: 2019
  ident: ref_13
  article-title: Parameter Uniform Method for a Singularly Perturbed System of Delay Differential Equations of Reaction–Diffusion Type with Integral Boundary Conditions
  publication-title: Int. J. Appl. Comput. Math.
  doi: 10.1007/s40819-019-0675-2
– volume: 307
  start-page: 606
  year: 2005
  ident: ref_18
  article-title: Numerical treatment of a mathematical model arising from a model of neuronal variability
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2005.02.014
– volume: 66
  start-page: 272
  year: 2006
  ident: ref_20
  article-title: Uniformly convergent non-standard finite difference methods for singularly perturbed differential-difference equations with delay and advance
  publication-title: Int. J. Numer. Methods Eng.
  doi: 10.1002/nme.1555
– volume: 2022
  start-page: 2037131
  year: 2022
  ident: ref_10
  article-title: A numerical scheme to solve mixed parabolic-elliptic problem involving singular perturbation
  publication-title: Int. J. Comput. Math.
– volume: 59
  start-page: 701
  year: 2018
  ident: ref_11
  article-title: Singularly perturbed delay differential equations of convection–diffusion type with integral boundary condition
  publication-title: J. Appl. Math. Comput.
  doi: 10.1007/s12190-018-1198-4
– volume: 81
  start-page: 49
  year: 2004
  ident: ref_19
  article-title: ε-Uniform fitted mesh method for singularly perturbed Differential-Difference equations mixed type of shifts with layer behavior
  publication-title: Int. J. Comput. Math.
  doi: 10.1080/00207160310001606052
– volume: 2021
  start-page: 6636607
  year: 2021
  ident: ref_21
  article-title: Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations
  publication-title: J. Math.
  doi: 10.1155/2021/6636607
– volume: 54
  start-page: 273
  year: 1994
  ident: ref_7
  article-title: Singular Perturbation Analysis of Boundary-Value Problems for Differential-Difference Equations. VI. Small Shifts with Rapid Oscillations
  publication-title: SIAM J. Appl. Math.
  doi: 10.1137/S0036139992228119
SSID ssj0002793507
Score 2.25378
Snippet Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this...
SourceID doaj
proquest
gale
crossref
SourceType Open Website
Aggregation Database
Enrichment Source
Index Database
StartPage 43
SubjectTerms Analysis
Bakhvalov–Shishkin mesh
Boundary conditions
Boundary layer
Boundary layers
Boundary value problems
Convergence
Decomposition
Delay
Differential equations
Finite difference method
finite difference scheme
fractional calculus
mixed-delay differential equations
Ordinary differential equations
Shishkin mesh
singular perturbation problems
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
  dbid: DOA
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3NT9swFLcQ4sAOiG2gdWPIB6RdiEjsJI6PbFDt0qpSQerNcuxntSMUaAoa__3eS9IKJAYXpCiRLCd6eX6f_vg9xo5Sq6BQtK1CS0xQPKSR9rGLXOwpYpZ5nrmm2IQaDovJRI-elPqiPWEtPHDLuJM4s2nwEHzIy7Qo0Z-qtMh0yKXHBgVkfWOlnyRTf5rlNC0x0mlhhiTm9SeBDh3ZqnmomHDS5DNX1CD2_88uN86mv8t2uiiRn7bUfWQbMP_EPgzWEKv1Z-aG9-1iS8XHyPhr4Bh-8jF6ItpYWj3yESzQnZTg-WD2F-9nUNlHftYVREHFrvj5XQv0zfEaT2f19Go255SZ8gHUU6j32GX__OLX76irmBC5VKhllIUyiSHPNASQUgbMf1SuICmC1E7qAEKUuvBpsCGglfOgvLIYIVhdiAQtndxnm_ObOXxhnKAbnRA6oQkP_IRFZZUadOJLq20e95hYMc-4Dk6cqlpUBtMK4rh5geM9drx-6bZF03i9-08alXVXgsJuGlBATCcg5i0B6bEfNKaGFBYJdLY7d4C_SdBX5lRhBEN2X_XYwWrYTafJtRHIQIFxkkq-vgc139g2FaxvJ3EO2OZycQ_f2ZZ7WM7qxWEjxP8Aio_5bQ
  priority: 102
  providerName: Directory of Open Access Journals
Title Numerical Scheme for Singularly Perturbed Mixed Delay Differential Equation on Shishkin Type Meshes
URI https://www.proquest.com/docview/2767208271
https://doaj.org/article/05a4fdefdf6b48b39974859f63d6b47e
Volume 7
WOSCitedRecordID wos000919612600001&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: 2504-3110
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0002793507
  issn: 2504-3110
  databaseCode: DOA
  dateStart: 20170101
  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: 2504-3110
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0002793507
  issn: 2504-3110
  databaseCode: M~E
  dateStart: 20170101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
– providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 2504-3110
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0002793507
  issn: 2504-3110
  databaseCode: M7S
  dateStart: 20171201
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 2504-3110
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0002793507
  issn: 2504-3110
  databaseCode: BENPR
  dateStart: 20171201
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Publicly Available Content Database
  customDbUrl:
  eissn: 2504-3110
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0002793507
  issn: 2504-3110
  databaseCode: PIMPY
  dateStart: 20171201
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwELag5QAHylMslJUPSFyImthJHJ-qPraCw64iFqRyihx73F0RdtvNFrX_npnEuwgJekGKEsl5yM6M5-XxN4y9S42CQlFahZbooDhII-1iG9nYkcUs8zyzXbEJNZkU5-e6DAG3NqRVbmRiJ6jd0lKM_ECoXAnUVyo5vLyKqGoUra6GEhr32S6hJCRd6t50G2MRyHxo7_RgQxK9-wNPW49M011UTGhp8g-F1OH2_0s6dyrnbO9_O_uEPQ7GJj_queMpuweLZ-zReIvU2j5ndnLdr9k0fIr0-wEcrVg-RYVG-anNLS9hhVqpBsfH8xs8n0JjbvlpqKuC8qHho6seL5zjMZ3N29n3-YKTg8vH0M6gfcG-no2-nHyMQuGFyKZCraPM10kMeabBg5TSoxuFA4Kk8FJbqT0IUevCpd54j8LSgXLKoKFhdCESFJjyJdtZLBfwinFCgLRC6ITiJvgJg3NeatCJq402eTxgYvP3KxtQyak4RlOhd0Ikq_5CsgH7sH3psgfluPvxYyLr9lFC1O4alquLKkzQKs5M6h145_M6LWq021RaZNrn0mGDggF7T0xR0bzHDloTti_gMAlBqzpSaAiR-lADtr9hiioIhLb6zRGv7779hj2kivZ9lGef7axX1_CWPbA_1_N2NWS7x6NJ-XnYhQ6GHbdjW_lpXH77BQpRCx4
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwELZKQaIceBaxUMAHEBeiJnYSxweECtuqVburSluk3oJjj9lVw2672QL7p_iNzOSxCAl66wEpSiQnseLkyzczfnzD2KvYKMgUTavQEgMUB3GgXWgDGzrymGWaJrZONqGGw-z0VB-vsZ_dWhiaVtlxYk3Ubmapj3xbqFQJtFcqen9-EVDWKBpd7VJoNLA4hOV3DNmqdwd9_L6vhdjbPfm4H7RZBQIbC7UIEl9EIaSJBg9SSo8xAlYNUealtlJ7EKLQmYu98R6ZwIFyyqAVNToTEbKBxHpvsJvoRghdTxUcrfp0BIId_atG3EhKHW57WupkyvqgQlJnk38YwDpPwL-sQW3i9u79by_nPrvbOtN8p0H_A7YG04fszmClRFs9YnZ42YxJlXyE-PwKHL10PkKDTfNvyyU_hjla3QIcH0x-4L4PpVnyfps3Bvmv5LsXjR46x200nlTjs8mUUwDPB1CNodpkn66llY_Z-nQ2hSeMk8KlFUJH1C-EVRjkNKlBR64w2qRhj4nua-e2VV2n5B9ljtEXQST_C0R67O3qpvNGdOTqyz8QjFaXkmJ4XTCbf8lbAsrDxMTegXc-LeKsQL9UxVmifSodFijosTcEwpx4DR_QmnZ5BjaTFMLyHYWOHplH1WNbHQjzlvCq_DcCn159-iW7vX8yOMqPDoaHz9iGQJ-x6dHaYuuL-SU8Z7fst8Wkmr-o_y3OPl83Xn8Bv-pk1g
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3Pb9MwFH4aHULjwG9EYYAPIC5ETew0jg8IDbqKarSqVJDGKTj2M60W2q3pgP5r_HU8J2kREuy2A1KUSInjxMmX773n2N8DeBZrian0wyqUoADFYhwoG5rAhNZ7zCJJuqZKNiFHo_T4WI134OdmLowfVrnhxIqo7cL4PvIOl4nkZK9k1HHNsIhxr__69CzwGaT8n9ZNOo0aIke4_k7hW_lq0KN3_Zzz_uGHt--CJsNAYGIuV0HX5VGISVehQyGEo3iBLoNR6oQyQjnkPFepjZ12jljBorRSk0XVKuURMYOgeq_ALrnkMW_B7ngwHH_a9vBwgj55W7XUkRAq7Dg_8UkX1UaGXqtN_GEOq6wB_7INlcHr3_yfH9UtuNG42eyg_i5uww7O78D14VajtrwLZnRe_60q2ISQ-xUZ-e9sQqbcj8wt1myMS7LHOVo2nP2gdQ8LvWa9JqMMMWPBDs9qpXRGy2Q6K6cnsznzoT0bYjnF8h58vJRW3ofWfDHHB8C89qXhXEW-x4iq0MR2QqGKbK6VTsI28M2bz0yjx-7TghQZxWUeLtlf4NKGl9uTTms5kouLv_GQ2hb1WuLVjsXyS9ZQUxZ2dewsOuuSPE5z8lhlnHaVS4SlHRLb8MIDMvOMRzdodDNxg5rptcOyA0kuoDecsg37G0BmDRWW2W80Prz48FO4RjDN3g9GR49gj5MzWXd17UNrtTzHx3DVfFvNyuWT5kNj8PmyAfsLi5FvDA
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+Scheme+for+Singularly+Perturbed+Mixed+Delay+Differential+Equation+on+Shishkin+Type+Meshes&rft.jtitle=Fractal+and+fractional&rft.au=Sekar+Elango&rft.au=Unyong%2C+Bundit&rft.date=2023-01-01&rft.pub=MDPI+AG&rft.eissn=2504-3110&rft.volume=7&rft.issue=1&rft.spage=43&rft_id=info:doi/10.3390%2Ffractalfract7010043&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2504-3110&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2504-3110&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2504-3110&client=summon