Advances in Difference Equations | |
An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations | |
article | |
Ali, Ihteram1  Haq, Sirajul1  Nisar, Kottakkaran Sooppy2  Baleanu, Dumitru3  | |
[1] Faculty of Engineering Sciences, GIK Institute;Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University;Department of Mathematics, Cankaya University;Institute of Space Sciences;Department of Medical Research, China Medical University Hospital, China Medical University | |
关键词: Lucas polynomials; Fibonacci polynomials; Finite differences; Stability analysis; | |
DOI : 10.1186/s13662-020-03160-4 | |
学科分类:航空航天科学 | |
来源: SpringerOpen | |
【 摘 要 】
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 θ-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$L_{\infty }$ ,$L_{2}$ , 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.
【 授权许可】
CC BY
【 预 览 】
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