A Chebyshev wavelet approach to the generalized time-fractional Burgers-Fisher equation

This work proposes a new method for obtaining the approximate solution of the time-fractional generalized Burgers Fisher equation. The method’s main idea is based on converting the nonlinear partial differential equation to a linear partial differential equation using the Picard iteration method. Then, the second kind Chebyshev wavelet collocation method is used to solve the linear equation obtained in the previous step. The technique is called the Chebyshev Wavelet Picard Method (CWPM). The proposed method successfully solves the time fractional generalized Burgers-Fisher equation. The obtained numerical results are compared with the exact solutions and with the solutions obtained using the Haar wavelet Picard method and the homotopy perturbation method.

Keywords:

Numerical methods for wavelets , fractional partial differential equations , Fractional derivatives and integrals , Picard iteration technique , Sylvester equation