Singularly perturbed initial value problems with robin initial conditions

Abstract

n this thesis, numerical methods are constructed for solving problems involving linear scalar newlineand systems of Singularly Perturbed Initial Value Problems with Robin Initial conditions. The newlinemethods constructed are proved to be parameter-uniform convergent in the maximum norm. newlineMany functional issues, such as mathematical boundary layer theory or approximation of newlinesolution of various problems represented by differential equations involving large or small para- newlinemeters, have become more complicated as Science and technology has progressed, necessitating newlinethe use of asymptotic approaches. The theory of asymptotic analysis for differential operators, newlineon the other hand, has predominantly been developed for frequent perturbations that are sub- newlineordinate to the unperturbed operator. In certain cases, the perturbations arise over a very small newlinearea, causing the dependent variable to adjust very quickly. newline