An operational matrix method for solving linear Fredholm--Volterra integro-differential equations

The aim of this paper is to propose an efficient method to compute approximate solutions of linear Fredholm‒Volterra integro-differential equations (FVIDEs) using Taylor polynomials. More precisely, we present a method based on operational matrices of Taylor polynomials in order to solve linear FVIDEs. By using the operational matrices of integration and product for the Taylor polynomials, the problem for linear FVIDEs is transformed into a system of linear algebraic equations. The solution of the problem is obtained from this linear system after the incorporation of initial conditions. Numerical examples are presented to show the applicability and the efficiency of the method. Wherever possible, the results of our method are compared with those yielded by some other methods.