Numerical solution of the system of second-order integro-differential equations using non-classical double sinc method

Abstract

This paper presents a new numerical technique based on the sinc-collocation approximation for solving of the system of second-order integro-differential equations with initial boundary conditions. The novelty of the approach consists on the usage of the weight functions in the traditional sinc-expansion. As it is known, the sinc basis functions are not differentiable at zero, so we modified the basis functions into a non-classical basis which is differentiable with zero derivative at the initial point. The properties of sinc-collocation are used to reduce the system of integro-differential equations into a system of algebraic equations. Furthermore, exponential convergence of the method is investigated which demonstrate its applicability in achieving the good accuracy. By solving some examples and comparing the results with existing methods the efficiency is examined.