An Improved Approach for Solutions of Systems of Linear Fredholm Integro Differential Equations

Abstract

In this paper, a numerical matrix method is used to solve the systems of high-order linear Fredholm integro-differential equations with variable coefficients under mixed conditions. The technique consists of collocation points and the Morgan-Voyce polynomials. The residual error functions of numerical solutions of the method are also presented. Firstly, the approximate solutions are formed and secondly, an error problem is constituted in favor of the residual error function. The numerical solutions are computed for this error problem by using the present method. The approximate solutions of the original problem and the error problem are the corrected Morgan-Voyce polynomial solutions. When the exact solutions of the problem are not known, the absolute errors can be approximately constructed through the approximate solutions of the error problem. Numerical examples are included to demonstrate the validity and the applicability of the technique, and also the results are compared with the different methods. All numerical computations have been performed using MATLAB v7.11.0 (R2010b).