Fitted Non-Polynomial Cubic Spline Method for Singularly Perturbed Delay Differential Equation Involving Two Small Parameters

Abstract

In this thesis, a numerical method for solving singularly perturbed delay differential equations involving two small parameters is presented. A fitted non-polynomial cubic spline scheme on a uniform mesh is developed. The stability and convergence of the proposed method have been established. The effect of the delay parameter (small shift) on the boundary layer(s) has also been analyzed and depicted in graphs. The applicability of the proposed scheme is validated by applying it to two model examples. Maximum absolute errors, in comparison with the results of other numerical experiments, are tabulated to illustrate the effectiveness of the proposed method.