A Collocation Method for Solving System of Volterra-differential-difference Equations with Terms of Chebyshev Polynomials

In this study, we present a numerical algorithm for solving systems of Volterra-differential-difference equations with variable coefficients by collocation method. This algorithm based on polynomial approximation, using the first kind Chebyshev polynomial basis with collocation method. This method transforms the system of Volterra-differential-difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. In addition, convergence analysis of the method is presented. Some cases of the mentioned equations are solved as examples to illustrate the reliability of the method. The results reveal that the method is very effective and accuracy.