Numerical Solutions of the Generalized Burgers‐Huxley Equation by a Differential Quadrature Method

Abstract

Numerical solutions of the generalized Burgers-Huxley equation are obtained using a polynomial differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time has been used. The computed results with the use of this technique have been compared with the exact solution to show the required accuracy of it. Since the scheme is explicit, linearization is not needed and the approximate solution to the nonlinear equation is obtained easily. The effectiveness of this method is verified through illustrative examples. The present method is seen to be a very reliable alternative method to some existing techniques for such realistic problems.

Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

“…Sari and Gurarslan [28] obtained the numerical solution of the GBH equation using a polynomial differential quadrature method. Malik et al [29] developed a heuristic scheme for the numerical solution of the GBF equation based on the hybridization of Exp-function method with nature inspired algorithm.…”

High-order finite difference schemes for numerical solutions of the generalized Burgers-Huxley equation

“…In the past few years, a great deal of effort has been spent to compute the solution of the Burgers-Huxley equation. Recently various powerful mathematical methods such as spectral methods [3][4][5], Adomian decomposition method [6][7][8], homotopy analysis method [9,10], the tanh-coth method [11], variational iteration method [12,13], Hopf-Cole transformation [14], differential quadrature method [15], meshless method [16] and factorization method [17] have been used in solving the equation.…”

Chebyshev Wavelet collocation method for solving generalized Burgers-Huxley equation

“…Chebyshev wavelet collocation method is applied to obtain approximate solution of the generalized Burgers–Huxley equation with the initial condition and boundary conditions for various values of α , β , γ , and δ . Comparing the results with exact solutions and approximate results, given in and , it can be shown that the represented method has the capability of solving the generalized Burgers–Huxley equation and also gives highly accurate solutions with minimal computational effort for both time and space.…”

“…Example This proposed method is applied to Equation for α = 1, β = 1, γ = 0.001, and the absolute errors for various values of δ are given in the Table , where M = 16 and k = 0 are taken. Comparisons of the maximal errors of present method, DQM , and Haar are given in the Table . The absolute errors for various values of M , k , and x are given in the Table where α = 1, β = 1, γ = 0.001, and δ = 1 are taken.…”

“…Also, Estevez and Gordoa applied a complete Painleve test to the generalized Burgers–Huxley equation. In the past few years, various mathematical methods such as spectral methods , Adomian decomposition method , homotopy analysis method , the tanh‐coth method , variational iteration method , Hopf‐Cole transformation , polynomial differential quadrature method , and high‐order finite difference schemes have been used to solve the equation. Lepik solved Burgers and sine‐Gordon equations by using the Haar wavelet method.…”