Distributional Solutions of Singularly Perturbed TwoPoint Boundary Value Problem

Abstract

In this thesis, distributional solution of singularly perturbed two point boundary value problem is presented. In order to achieve this goal, some important terminologies related to distribution are defined together with their properties. Homogeneous solution to singularly perturbed two point boundary value problem under consideration is described and then Green’s function was constructed in the sense of distribution to get the particular solution using convolution or without applying convolution. To verify the applicability of the method, three numerical examples were considered and solved. Using the developed method, problems with known exact solution is solved and it agrees with existing exact solution. Furthermore, using the developed method, problems with unknown exact solution is also solved. Finally, MATLAB simulation was implemented for various values of perturbation parameter in order to see the effect of this parameter and the nature of the layer created due to this parameter.