Solution of a system of delay differential equations of multi pantograph type

A collocation method is proposed to obtain an approximate solution of a system of multi pantograph type delay differential equations with variable coefficients subject to the initial conditions. The general approach is that, first of all the solution of the system has been expanded according to First Boubaker polynomials (FBPs) basis. Then, by employing the matrix operations and collocation nodes, the original problem and the associated initial conditions are reduced to a nonlinear system. By solving such system, the unknown coefficients of the approximate solution can be determined. Convergence analysis of the proposed method has been proved. The presented method has been tested of three different examples. The computed results confirm the high accuracy of collocation method based on FBPs.