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