Author:
Ali Ihteram,Haq Sirajul,Nisar Kottakkaran Sooppy,Baleanu Dumitru
Abstract
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 withθ-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∞,$L_{2}$L2, 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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