High-order solution of Generalized Burgers–Fisher Equation using compact finite difference and DIRK methods

Abstract The main goal of this paper is to developed a high-order and accurate method for the solution one-dimensional generalized Burgers-Fisher with Numman boundary conditions. We combined between fourth-order compact finite difference scheme spatial part diagonal implicit Runge Kutta in temporal part. In addition, we discretized points by using terms fourth order accuracy. This combine leads ordinary differential equation which will take full advantage line (MOL). Some numerical experiments presented show that combination give an reliable solving problems.