Chelyshkov collocation approach to solve the systems of linear functional differential equations

In this paper, we present a new collocation method based on Chelyshkov polynomials for solving the system of functional differential equations under the initial-boundary conditions.By means of Chelyshkov polynomials and collocation points, this method converts the so-called system into a matrix equation, which involves the unknown Chelyshkov coeffcients. We give some illustrative examples, which arise in physics, biology, chemistry and mechanics and so on, to indicate the reliability and efficiency of the method. Also, a technique based on residual functions is performed to check the accuracy of the problem.