Alternating direction implicit method for singularly perturbed 2D parabolic convection-diffusion-reaction problem with two small parameters

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dc.authorid0000-0001-7527-1989
dc.authorid0000-0002-7533-5601
dc.authorid0000-0001-8628-5497
dc.contributor.authorMrityunjoy, B.
dc.contributor.authorNatesan, S.
dc.contributor.authorSendur, A.
dc.date.accessioned2026-01-24T12:31:25Z
dc.date.available2026-01-24T12:31:25Z
dc.date.issued2023
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractIn this article, we construct and analyse an Alternating Direction Implicit (ADI) scheme for singularly perturbed 2D parabolic convection-diffusion-reaction problems with two small parameters. We consider the operator-splitting ADI finite difference scheme for time stepping on a uniform mesh and a simple upwind-difference scheme for spatial discretization on a specially designed piecewise-uniform Shishkin mesh. The resulting scheme is proved to be uniformly convergent of order O(N-1 In N + M-1), where N, M are the spatial and temporal parameters respectively. Numerical experiments confirm the theoretical results and the effectiveness of the proposed method.
dc.identifier.doi10.1080/00207160.2022.2114077
dc.identifier.endpage282
dc.identifier.issn0020-7160
dc.identifier.issn1029-0265
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85138314432
dc.identifier.scopusqualityQ2
dc.identifier.startpage253
dc.identifier.urihttps://doi.org/10.1080/00207160.2022.2114077
dc.identifier.urihttps://hdl.handle.net/20.500.12868/5847
dc.identifier.volume100
dc.identifier.wosWOS:000854941800001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherTaylor & Francis Ltd
dc.relation.ispartofInternational Journal of Computer Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260121
dc.subjectSingularly perturbed 2D parabolic convection-reaction-diffusion problem
dc.subjectalternating direction implicit scheme
dc.subjectfinite difference scheme
dc.subjectShishkin meshes
dc.subjectstability
dc.subjectuniform error estimate
dc.titleAlternating direction implicit method for singularly perturbed 2D parabolic convection-diffusion-reaction problem with two small parameters
dc.typeArticle

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