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Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay

ArticleAçık Erişim

Özet

In this paper, the initial value problem for a quasilinear singularly perturbed delay Volterra integro-differential equation was considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form, a fitted difference scheme is constructed and analysed. It is shown that the method displays first order uniform convergence in perturbation parameter. Some numerical results are given to confirm the theoretical analysis. © 2019 Elsevier B.V.

Anahtar Kelimeler

Finite difference methodSingular perturbationUniform convergenceVolterra delay-integro-differential equationInitial value problemsIntegrodifferential equationsNonlinear equationsPerturbation techniquesConvergence analysisExponential basis functionsPerturbation parametersSingular perturbationsSingularly perturbedVolterraVolterra integro-differential equationsConvergence of numerical methods
RDL Kalıcı Bağlantı (PID)
https://rdlopen.rawdatalibrary.net/r/ebyu/13692Resmi atıflarda kullanılan kalıcı adres
DOI
https://doi.org/10.1016/j.cam.2019.01.026Yayıncı resmi DOI adresi
Tam Kayıt
AlanDeğerDil
dc.contributor.authorYapman, Ömer
dc.contributor.authorAmiraliyev, Gabil M.
dc.contributor.authorAmirali, Ilhame
dc.date.accessioned2026-10-18T20:28:31.328958199Z
dc.date.available2026-10-18T20:28:31.328958199Z
dc.date.issued2019
dc.description.abstractIn this paper, the initial value problem for a quasilinear singularly perturbed delay Volterra integro-differential equation was considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form, a fitted difference scheme is constructed and analysed. It is shown that the method displays first order uniform convergence in perturbation parameter. Some numerical results are given to confirm the theoretical analysis. © 2019 Elsevier B.V.
dc.identifier.doi10.1016/j.cam.2019.01.026
dc.identifier.eissn1879-1778
dc.identifier.endpage309
dc.identifier.issn0377-0427
dc.identifier.scopus2-s2.0-85061796536
dc.identifier.startpage301
dc.identifier.urihttps://rdlopen.rawdatalibrary.net/r/ebyu/13692
dc.identifier.volume355
dc.identifier.wosWOS:000463302400022
dc.language.isoen
dc.publisherElsevier B.V.
dc.relation.ispartofJournal of Computational and Applied Mathematics
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectFinite difference method
dc.subjectSingular perturbation
dc.subjectUniform convergence
dc.subjectVolterra delay-integro-differential equation
dc.subjectInitial value problems
dc.subjectIntegrodifferential equations
dc.subjectNonlinear equations
dc.subjectPerturbation techniques
dc.subjectConvergence analysis
dc.subjectExponential basis functions
dc.subjectPerturbation parameters
dc.subjectSingular perturbations
dc.subjectSingularly perturbed
dc.subjectVolterra
dc.subjectVolterra integro-differential equations
dc.subjectConvergence of numerical methods
dc.titleConvergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay
dc.typeArticle
dspace.entity.typePublication
rdl.citation.scopus45
rdl.citation.wos44
rdl.oa.statusgreen
rdl.source.indexSCOPUS
rdl.source.indexWOS
rdl.wos.indexScience Citation Index Expanded (SCI-EXPANDED)