Polynomial solution of the most general linear Fredholm–Volterra integrodifferential-difference equations by means of Taylor collocation method

Abstract

In this paper, a Taylor collocation method has been presented for numerically solving the high-order general linear Fredholm–Volterra integrodifferential-difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. Using the Taylor collocation points, the method transforms the equation and conditions into the matrix equations with the unknown Taylor coefficients and hence by finding the Taylor coefficients, the polynomial approach is obtained. Also, to illustrate the accuracy of the method, numerical examples are presented and the results are discussed.