Numerical Treatment of Non-Linear singular pertubation problems
This thesis deals with the design and implementation of some novel numerical methods for non-linear singular pertubations problems (NSPPs). It provide a survey of asymptotic and numerical methods for some NSPPs in the past decade. By considering two test problems, rigorous asymptotic analysis is carried out. Based on this analysis, suitable numerical methods are designed, analyzed and implemented in order to have some relevant results of physical importance. Since the asymptotic analysis provides only qualitative information, the focus is more on the numerical analysis of the problem which provides the quantitative information.
Non-linear Singular Perturbation Problems, Asymptotic Analysis, Fitted Mesh Finite Difference Methods, Fitted Operator Finite Difference Methods, Stability
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