Explicit analytical solutions of the generalized Burger and Burger–Fisher equations by homotopy perturbation method

Abstract

In this article, we apply the homotopy perturbation method (HPM) to obtain approximate analytical solutions of the generalized Burger and Burger-Fisher (B-F) equations. Several numerical examples are given to illustrate the efficiency of the HPM. Comparison of the result obtained by the present method with exact solution reveals that the accuracy and fast convergence of the new method. It is predicted that the HPM can be found wide application in engineering problems.

Implementation of Wavelet Based Transform for numerical solutions of Partial differential equations

“…The Burgers-Fisher equation which describes the interaction between the reaction mechanism, convection effect, and diffusion transport [6] is considered in this paper. Many numerical schemes have been proposed for obtaining approximate solutions of the Burger-fisher equation [7][8][9][10][11][12].…”

“…In this work, the goal is to obtain the approximate solution of the Burger-Fisher equation by using the Haar wavelet method [13][14] and to compare the obtaining results with the exact solution and the iterative methods [15]. Let us consider the Burger-Fisher equation [10] is as follows:-…”

Application of modifed optimal homotopy perturbation method to higher order boundary value problems in a nite domain

“…In literature we come across dierent analytic methods. Some of the interesting analytic methods which can be applied to a wide range of high order dierential equations are homotopy analysis method (HAM) [2][3][4], homotopy perturbation method (HPM) [5][6], Adomian decomposition method (ADM) [7], optimal homotopy asymptotic method (OHAM) [8][9][10][11][12], optimal homotopy perturbation method (OHPM) [13][14][15] and variational iteration method (VIM) [16][17][18]. In order to obtain best approximate solution of dierential equations, researchers in the eld modify the existing analytical methods time to time.…”

A New Reliable Approach for Two-Dimensional and Axisymmetric Unsteady Flows Between Parallel Plates

“…The HPM is in fact a coupling of the traditional perturbation method and homotopy in topology [21]. This method was applied to axisymmetric flow over a stretching sheet [22], thermal boundary-layer problems in a semi-infinite plate [23], nonlinear JefferyHamel flow [24], coupled nonlinear partial differential equations [25], Abel integral equation [26], peristaltic flow of a magnetohydrodynamic (MHD) Newtonian fluid in an asymmetric channel [27], MHD flow over a nonlinear stretching sheet [28], generalized Burger and Burger-Fisher equations [29], wave and nonlinear diffusion equations [30], time-fractional reaction-diffusion equation of Fisher type [31], motion of a spherical solid particle in plane coquette fluid flow [32], and heat transfer of copper-water nanofluid flow between parallel plates [33]. Natural convection heat transfer of a copper-water nanofluid in a cold outer circular enclosure containing a hot inner sinusoidal circular cylinder in the presence of a horizontal magnetic field was investigated numerically using the control volume based finite element method (CVFEM) [34].…”