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.
