Sixth-order stable central difference method for self-adjoint singularly perturbed two-point boundary value problems

Abstract

In this thesis, sixth order stable central difference method has been presented for solving selfadjoint singularly perturbed two-point boundary value problems. First the given interval is discretized and the derivatives of the given differential equation are replaced by the central difference approximations. Then, the given differential equation is transformed to linear system of algebraic equations. Further, this algebraic system is transformed into the three term recurrence relation, which can easily be solved by using Thomas Algorithm. To validate the applicability of the proposed method, some model examples have been considered and solved for different values of perturbation parameter and mesh sizes. The stability and convergence of the method have been analyzed. As it can be observed from the numerical results in tables and graphs, the presented method approximates the exact solutions very well and provides better results than some existing numerical methods reported in the literature.