Accelerated Method for Singularly Perturbed Burgers Equatio

Abstract

This thesis presents an e cient numerical method for solving the sin gularly perturbed Burgers equation, achieved by transforming the original nonlinear problem into a linear form through quasilineariza tion. Utilizing central nite di erence approximations on a uniformly discretized mesh, the method enhances accuracy via Richardson ex trapolation, raising the order of convergence from second-order to fourth-order. Stability and consistency are ensured through a de tailed Von-Neumann stability analysis, con rming the methods re liability. Demonstrated through various example problems, the nu merical results reveal superior accuracy and faster convergence com pared to existing techniques, with a notable reduction in maximum absolute error as the number of mesh points increases.