Numerical solution of singularly perturbed self-adjoint boundary value problem using galerkin method

Abstract

In this thesis, numerical solution of self-adjoint Boundary value problems has been presented for solving second order singularly perturbed problem using Galerkin method. First, for the given problem, the residue was computed using appropriate approximated basis function which satisfies all the boundary conditions. Then, using the chosen weighting function integrating the weighted residue over the domain and the given differential equation is transformed to linear systems of algebraic equations. Further, these algebraic equations were to solved by using Galerkin method. To validate the applicability of the proposed method, two model examples have been considered and solved for different values of perturbation parameter and with different order of basis function. Additionally convergence of error bounds has been established for the method. As it can be observed from the numerical results presented in Tables and graphs, the present method approximates the exact solution very well. Moreover, the present method gives better results when the order of basis function is increased than some existing numerical method reported in the literature.