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An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations

dc.contributor.authorAli, Ihteram
dc.contributor.authorHaq, Sirajul
dc.contributor.authorNisar, Kottakkaran Sooppy
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorID56389tr_TR
dc.date.accessioned2022-03-16T10:39:15Z
dc.date.available2022-03-16T10:39:15Z
dc.date.issued2021
dc.departmentÇankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractWe propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, the temporal part is discretized by finite difference method together with theta-weighted scheme. Then, for the approximation of spatial part of unknown function and its spatial derivatives, we use a mixed approach based on Lucas and Fibonacci polynomials. With the help of these approximations, we transform the nonlinear partial differential equation to a system of algebraic equations, which can be easily handled. We test the performance of the method on the generalized Burgers-Huxley and Burgers-Fisher equations, and one- and two-dimensional coupled Burgers equations. To compare the efficiency and accuracy of the proposed scheme, we computed L-infinity, L-2, and root mean square (RMS) error norms. Computations validate that the proposed method produces better results than other numerical methods. We also discussed and confirmed the stability of the technique.en_US
dc.description.publishedMonth1
dc.identifier.citationAli, Ihteram...et al. (2021). "An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations", Advances in Difference Equations, Vol. 2021, No. 1.en_US
dc.identifier.doi10.1186/s13662-020-03160-4
dc.identifier.issn1687-1839
dc.identifier.issue1en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/5119
dc.identifier.volume2021en_US
dc.language.isoenen_US
dc.relation.ispartofAdvances in Difference Equationsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectLucas Polynomialsen_US
dc.subjectFibonacci Polynomialsen_US
dc.subjectFinite Differencesen_US
dc.subjectStability Analysisen_US
dc.titleAn efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equationstr_TR
dc.titleAn Efficient Numerical Scheme Based on Lucas Polynomials for the Study of Multidimensional Burgers-Type Equationsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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