A new numerical scheme for solving system of Volterra integro-differential equation

Abstract

In this article, we apply Genocchi polynomials to solve numerically a system of Volterra integro-differential equations. This is done by approximating functions using Genocchi polynomials and derivatives using Genocchi polynomials operational matrix of integer order derivative. Combining approximation with collocation method, the problem is reduced to a system of algebraic equations in terms of Genocchi coefficients of the unknown functions. By solving the Genocchi coefficients, we obtain good approximate functions of the exact solutions of the system. A few numerical examples show that our proposed Genocchi polynomials method achieves better accuracy compared to some other existing methods. Keywords: System of Volterra integro-differential equations, Genocchi polynomials, Operational matrix of integer order derivative