Trigonometric Spline Method for the Numerical Solutions of Singularly Perturbed Volterra Integro-Differential Equations

Abstract

In this study, the trigonometric spline function is presented for solving a singularly perturbed initial value problem for a linear first-order Volterra integro-differential equation. By this idea integro-differential equation will be changed into thesystem of algebraic equation. The relations and the error analysis of trigonometric spline function are derived. The convergence analysis of the method discussed. Some examples are included to demonstrate the validity and applicability of the technique and to compare the computed results with the existing methods.