Application of Optimal Homotopy Asymptotic Method to Burger Equations

Abstract

We apply optimal homotopy asymptotic method (OHAM) for finding approximate solutions of the Burger's-Huxley and Burger's-Fisher equations. The results obtained by proposed method are compared to those of Adomian decomposition method (ADM) (Ismail et al., (2004)). As a result it is concluded that the method is explicit, effective, and simple to use.

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

“…In Table 9, we tabulate a comparison between HBSCM and the existing methods CFDS [26], FONS [33], ADM [38], Galerkin method (GM) [44], higher order finite difference method (HFDM) [52], MCBS [55], cubic B-spline algorithm (CBSA) [56], and optimal homotopy asymptotic method (OHAM) [69] at = 1, 3. Computations of the absolute errors and two different types of error norms have been mentioned in Tables 10 and 11, respectively.…”

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

“…The entire computational work has been done with the help of MATLAB software. Example 1: Let us consider the Burger-Fisher equation (1), with the initial and boundary conditions in quations (2) and (3) respectively and the exact solution given in equation (4). Table (1) shows the approximate solution using the proposed method against the exact solution when = 0.01, = 0.01, and = 1, whereas Table (2) shows a comparison between the absolute error of the solution by the proposed method and the absolute error by using the variational iteration method [15] for different values of x and t when = 0.001, = 0.001, and = 1.…”

“…The numerical solutions of NPDEs, such as the Burgers-Fisher equation, have attracted much attention due to their potential applications in various fields of fluid dynamics, heat conduction, gas dynamic, traffic flow, applied mathematics and some other fields of science [1][2][3][4][5]. The Burgers-Fisher equation which describes the interaction between the reaction mechanism, convection effect, and diffusion transport [6] is considered in this paper.…”

“…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].…”

Application of OHAM-DJ to the System of Burgers’ Equations

“…This method has been studied by a number of researchers for solving linear and nonlinear partial differential equations [20]- [23]. In [24]- [27] proved OHAM is more efficient to solve Burgers' equations. In 2006, a new method by Daftardar-Gejji and Jafari for solving nonlinear functional appeared [28].…”