An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations
dc.contributor.author | Ali, Ihteram | |
dc.contributor.author | Haq, Sirajul | |
dc.contributor.author | Nisar, Kottakkaran Sooppy | |
dc.contributor.author | Baleanu, Dumitru | |
dc.contributor.authorID | 56389 | tr_TR |
dc.date.accessioned | 2022-03-16T10:39:15Z | |
dc.date.available | 2022-03-16T10:39:15Z | |
dc.date.issued | 2021 | |
dc.department | Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü | en_US |
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. | en_US |
dc.description.publishedMonth | 1 | |
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. | en_US |
dc.identifier.doi | 10.1186/s13662-020-03160-4 | |
dc.identifier.issn | 1687-1839 | |
dc.identifier.issue | 1 | en_US |
dc.identifier.uri | http://hdl.handle.net/20.500.12416/5119 | |
dc.identifier.volume | 2021 | en_US |
dc.language.iso | en | en_US |
dc.relation.ispartof | Advances in Difference Equations | en_US |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject | Lucas Polynomials | en_US |
dc.subject | Fibonacci Polynomials | en_US |
dc.subject | Finite Differences | en_US |
dc.subject | Stability Analysis | en_US |
dc.title | An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations | tr_TR |
dc.title | An Efficient Numerical Scheme Based on Lucas Polynomials for the Study of Multidimensional Burgers-Type Equations | en_US |
dc.type | Article | en_US |
dspace.entity.type | Publication |