A parameter-uniform hybrid method for singularly perturbed parabolic 2D convection-diffusion-reaction problems

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dc.authorid0000-0001-8628-5497
dc.authorid0000-0002-7533-5601
dc.authorid0000-0001-7527-1989
dc.contributor.authorBarman, Mrityunjoy
dc.contributor.authorNatesan, Srinivasan
dc.contributor.authorSendur, Ali
dc.date.accessioned2026-01-24T12:31:07Z
dc.date.available2026-01-24T12:31:07Z
dc.date.issued2025
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractThe solution of the singular perturbation problems (SPP) of convection-diffusion-reaction type may exhibit regular and corner layers in a rectangular domain. In this work, we construct and analyze a parameter-uniform operator-splitting alternating direction implicit (ADI) scheme to efficiently solve a two-dimensional parabolic singularly perturbed problem with two positive parameters. The proposed model is a combination of the backward-Euler method defined on a uniform mesh in time and a hybrid method in space defined on a special Shishkin mesh. The analysis is presented on a layer adapted piecewise-uniform Shishkin mesh. The developed numerical method is proved to be first-order convergent in time and almost second-order convergent in space. The numerical experiments are performed to validate the theoretical convergence results and illustrate the efficiency of the current strategy.
dc.description.sponsorshipThe authors express their sincere thanks to the referees whose valuable comments helped to improve the presentation.
dc.identifier.doi10.1016/j.apnum.2024.08.026
dc.identifier.endpage135
dc.identifier.issn0168-9274
dc.identifier.issn1873-5460
dc.identifier.scopus2-s2.0-85203009611
dc.identifier.scopusqualityQ1
dc.identifier.startpage111
dc.identifier.urihttps://doi.org/10.1016/j.apnum.2024.08.026
dc.identifier.urihttps://hdl.handle.net/20.500.12868/5635
dc.identifier.volume207
dc.identifier.wosWOS:001309040100001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofApplied Numerical Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260121
dc.subjectSingularly perturbed IBVP
dc.subjectConvection-diffusion-reaction
dc.subjectShishkin mesh
dc.subjectADI scheme
dc.subjectError estimate
dc.titleA parameter-uniform hybrid method for singularly perturbed parabolic 2D convection-diffusion-reaction problems
dc.typeArticle

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