Non-Polynomial Septic Spline Method for Third Order Type Singularly Perturbed Boundary Value Problems

Abstract

In this thesis, we present non-polynomial septic spline method for solving third order type singularly perturbed boundary value problems. First, the given system is discretized. Then, the spline coefficients are derived and the consistency relation is obtained by using continuity of second, fourth and fifth derivatives. Further, we reduce the obtained fifteen different systems of equations to a system of equations and develop boundary equation in order to equate system of linear equations. The convergence analysis of the obtained hepta-diagonal scheme is investigated. To validate the applicability of the method, two model examples have been considered for different values of perturbation parameter  and different mesh size h. The numerical results are presented in Tables and Figures and compared with some existing numerical method in the literature. Further, the proposed method approximate the exact solution very well when h   , for which most of the existing methods reported in the literature fail to give good result.