Abstract
In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers—Fisher equation. The method is based on the direct weak formulation of the Burgers—Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge—Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.
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