An efficient and reliable numerical study for the 2 D nonlinear coupled Burgers equation simulating many physical phenomena

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dc.contributor.authorOzer, Sibel
dc.contributor.authorKutluay, Selcuk
dc.date.accessioned2026-04-04T13:33:17Z
dc.date.available2026-04-04T13:33:17Z
dc.date.issued2026
dc.departmentİnönü Üniversitesi
dc.description.abstractIn this paper, an accurate and reliable fully discretized linear numerical scheme has been developed for solving two-dimensional nonlinear coupled Burgers equation given by pre-defined initial and boundary values. The scheme is constructed based on the weighted finite differences utilizing a Richtmyer-type linearization in place of nonlinear terms appearing in the two-dimensional nonlinear coupled Burgers equation. It should be known that this linearization is used for the first time in this study for a two-dimensional nonlinear coupled partial differential equation. The performance and reliability of the present method are verified using four different widely-used examples, three of which have exact solutions and one has no an exact solution. To make sure that the current scheme exhibits good results, some error norms and convergence rate of the obtained approximate numerical solutions for each example are calculated and a comparison is made with other ones existing in the literature for the same parameter values. It has also been shown that the scheme is unconditionally stable for 0.5 <=theta <= 1.
dc.identifier.doi10.1142/S0129183125500512
dc.identifier.issn0129-1831
dc.identifier.issn1793-6586
dc.identifier.issue1
dc.identifier.orcid0000-0003-4956-4002
dc.identifier.scopus2-s2.0-105000761435
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1142/S0129183125500512
dc.identifier.urihttps://hdl.handle.net/11616/109061
dc.identifier.volume37
dc.identifier.wosWOS:001447614400001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherWorld Scientific Publ Co Pte Ltd
dc.relation.ispartofInternational Journal of Modern Physics C
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WOS_20250329
dc.subject2D nonlinear coupled Burgers equation
dc.subjectlinearized implicit finite difference
dc.subjectRichtmyer-type linearization
dc.subjectstability analysis
dc.titleAn efficient and reliable numerical study for the 2 D nonlinear coupled Burgers equation simulating many physical phenomena
dc.typeArticle

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