On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods

Abstract

Two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM), are presented. Haar wavelet method is an efficient numerical method for the numerical solution of arbitrary order partial differential equations like BurgersFisher and generalized Fisher equations. The approximate solutions thus obtained for the fractional Burgers-Fisher and generalized Fisher equations are compared with the optimal homotopy asymptotic method as well as with the exact solutions. Comparison between the obtained solutions with the exact solutions exhibits that both the featured methods are effective and efficient in solving nonlinear problems. The obtained results justify the applicability of the proposed methods for fractional order Burgers-Fisher and generalized Fisher's equations.

Application of the Exp-function method for solving the combined KdV-mKdV and Gardner-KP equations

“…In order to verify whether the proposed algorithm leads to greater accuracy, the numerical solutions have been evaluated. From results, we can certainly conclude that the proposed technique provides remarkable exactness in comparison with the method available in the literature [16,17]. Figure 3 depicts the q-HATM solution for different values of auxiliary parameter ℏ which helps us to control and adjust the convergence region.…”

“…Description of numerical solutions derived from Haar wavelet method[17], OHAM[17] and present method with exact solution at = 1, h = −1, = 0.01 and n = 1 (Example 4.2)…”

A numerical investigation of time-fractional modified Fornberg–Whitham equation for analyzing the behavior of water waves

“…To demonstrate the basic ideas of optimal homotopy asymptotic method [11][12][13][14][15], consider the following general nonlinear differential equation…”

Finite element analysis and approximation of Burgers’‐Fisher equation

“…For example, Adomian decomposition method (ADM) , homotopy analysis method (HAM) , homotopy perturbation method (HPM) , variation iteration method (VIM) , tanh‐coth method , Exp‐function method , and so on. are some of the analytical methods whereas Haar wavelet method , spectral collocation method , collocation method using radial basis , spectral domain decomposition approach , finite difference method , finite difference based pseudospectral approach , and so on fall in the category of numerical methods.…”