A semi-analytical algorithm to solve systems of integro-differential equations under mixed boundary conditions

In this work we present a semi-analytical method to solve systems of integro-differential equations under mixed boundary conditions. The proposed method handles linear and nonlinear systems of Fredholm-Volterra integro-differential equations in a reliable manner. We present a convergence analysis for the proposed method to emphasize its reliability. Numerical examples are examined to show the efficiency and the accuracy of the scheme. We show that a few number of approximating terms gives results of high accuracy level, and by increasing the number of these terms, the error of the approximated solution decreases rapidly. The proposed method is powerful and reliable to solve other kinds of systems of integro-differential equations. Further, it has a small CPU time and its computational time is less than the other methods.