Linear Fredholm Integro-Differential-Difference Equations and Their Effective Computation

Abstract

In this work, a new computational approach is proposed to solve the linear Fredholm integro-differential-difference equations with variable coefficients under the mixed conditions. This method yields the solution of the governing equation with the form of a linear combination of a special kind of basis functions. Those unknown coefficients of the solution of the given problem are determined by solving a linear system of algebraic equations which has been derived with the help of the least square approximation method and the Lagrange-multiplier method. Moreover, an error estimation of the approximate solution is constructed by using the residual error function technique. The convergence of the approximate solution is proved. Several numerical examples are given to demonstrate the accuracy and efficiency. Comparisons are made between the proposed method and other existing approaches.