A new collocation approach for solving systems of high-order linear Volterra integro-differential equations with variable coefficients

This paper contributes an efficient numerical approach for solving the systems of high-order linear Volterra integro-differential equations with variable coefficients under the mixed conditions. The method we have used consists of reducing the problem to a matrix equation which corresponds to a system of linear algebraic equations. The obtained matrix equation is based on the matrix forms of Fibonacci polynomials and their derivatives by means of collocations. In addition, the method is presented with error. Numerical results with comparisons are given to demonstrate the applicability, efficiency and accuracy of the proposed method. The results of the examples indicated that the method is simple and effective, and could provide an approximate solution with high accuracy or exact solution of the system of high-order linear Volterra integro-differential equations.