An Improved Algorithm for the Solution of Generalized Burger-Fishers Equation

Abstract

In this paper, an improved algorithm for the solution of Generalized Burger-Fisher's Equation is presented. A Maple code is generated for the algorithm and simulated. It was observed that the algorithm gives the solution with less computation. The solution gives a better result when compared with the numerical solutions in the existing literature.

Nonstandard finite‐difference scheme to approximate the generalized Burgers‐Fisher equation

“…It is noticeable that increasing stepsizes do not decrease accuracy of the scheme significantly. These comparisons show that the NSFD1 scheme has good efficiency even for high stepsize.In Tables and , we present the absolute errors of the computed solution for the BF equation, by Adomin decomposition method (ADM), VI, MVI, CBRBF, and EF methods, together with those of the NSFD1 scheme. Tables and present maximum absolute errors for various values of a and k with time stepsize Δ t = 0.0005.…”

“…One of the important nonlinear PDEs, which appears in various applications, such as fluid dynamics, shock wave formation, turbulence, heat conduction, traffic flow, gas dynamics, and some other fields of science, is the Burgers‐Fisher (BF) equation. () In this paper, we consider the BF equation of the form where the coefficients a , k , and b are constants. Throughout this paper, we assume that a and k are nonnegative and b is positive.…”

“…One of the important nonlinear PDEs, which appears in various applications, such as fluid dynamics, shock wave formation, turbulence, heat conduction, traffic flow, gas dynamics, and some other fields of science, is the Burgers-Fisher (BF) equation. [1][2][3] In this paper, we consider the BF equation of the form…”

“…In the literature, several methods have been proposed to solve the BF equation from either numerically or analytically points of view. Among these schemes, we can mention the local discontinuous Galerkin (LDG) method, modified variational iteration (MVI) and variational iteration (VI) methods, spectral collocation and spectral domain decomposition (SDD) methods,() collocation method based on radial base functions (CBRBFs), Exp‐function (EF) method, and modified cubic B‐splines (MCBSs), though for more study about the BF equation, one may refer to Wazwaz, Mickens and Gumel, and Kaya and El‐Sayed and the references therein. Nonstandard finite‐difference (NSFD) schemes, introduced by Mickens to solve ordinary differential equations and PDEs,() have been proved to be one of the most efficient methods in recent years .…”

A robust scheme based on novel‐operational matrices for some classes of time‐fractional nonlinear problems arising in mechanics and mathematical physics

“…Absolute error comparison for M = 8, k = 1 and r = iterations with existing results[37,41,[53][54][55][56] when = = 1, = 3, = 0 for different values of x and t…”