dc.contributor.author |
Ali, Ihteram
|
|
dc.contributor.author |
Haq, Sirajul
|
|
dc.contributor.author |
Nisar, Kottakkaran Sooppy
|
|
dc.contributor.author |
Baleanu, Dumitru
|
|
dc.date.accessioned |
2022-03-16T10:39:15Z |
|
dc.date.available |
2022-03-16T10:39:15Z |
|
dc.date.issued |
2021-01-11 |
|
dc.identifier.citation |
Ali, 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. |
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dc.identifier.issn |
1687-1839 |
|
dc.identifier.uri |
http://hdl.handle.net/20.500.12416/5119 |
|
dc.description.abstract |
We 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. |
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dc.language.iso |
eng |
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dc.relation.isversionof |
10.1186/s13662-020-03160-4 |
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dc.rights |
info:eu-repo/semantics/openAccess |
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dc.subject |
Lucas Polynomials |
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dc.subject |
Fibonacci Polynomials |
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dc.subject |
Finite Differences |
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dc.subject |
Stability Analysis |
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dc.title |
An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations |
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dc.type |
article |
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dc.relation.journal |
Advances in Difference Equations |
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dc.contributor.authorID |
56389 |
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dc.identifier.volume |
2021 |
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dc.identifier.issue |
1 |
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dc.contributor.department |
Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü |
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