Solving nonlinear Burgers’ equation with semi-approximate approach using modified Gauss-Seidel iteration

The main purpose of this article is to investigate the formulation and implementation of Modified Gauss-Seidel (MGS) iteration using semi-approximate approach to solve the one-dimensional (1D) nonlinear Burgers’ equation. To do that, this problem needs to be discretized by using the second-order implicit finite difference scheme and the semi-approximate approach in order to get the second-order semi-approximate implicit approximation equation which leads to a sparse and huge scale linear system. Then, this linear system has been solved via the proposed MGS iteration. Four examples are presented to analyze the performance of MGS iteration. Then numerical experiments have been carried out on four examples of problems to verify the performance of MGS iteration.