A spectral domain decomposition approach for the generalized Burger’s–Fisher equation

In this study, we use the spectral collocation method using Chebyshev polynomials for spatial derivatives and fourth order Runge–Kutta method for time integration to solve the generalized Burger’s–Fisher equation (B–F). Firstly, theory of application of Chebyshev spectral collocation method (CSCM) and domain decomposition on the generalized Burger’s–Fisher equation is presented. This method yields a system of ordinary differential algebraic equations (DAEs). Secondly, we use fourth order Runge–Kutta formula for the numerical integration of the system of DAEs. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method.