Legendre pseudo-spectral method for solving multi-pantograph delay differential equations

Delay differential equations have a wide range of applications in science and engineering. When these equations are nonlinear and complex the exact solution can usually not be calculated. So finding a numerical solution with high precision for these equations is essential. In this paper we present a numerical method based on the transferred Legendre polynomials to solve multiple pantograph delay differential equations. In this method we use the Legendre-Gauss-Lobato collocation points to discretize the problem and turn the problem into a nonlinear programming problem. From solving this nonlinear programming problem we get an approximate solution for the the main multiple pantograph delay differential equation. We analyse the feasibility of the nonlinear programming problem and the convergence of the obtained approximate solution to the exact solution. In addition by solving several numerical examples and comparing the method with other methodsWe show the efficiency and the capability of the proposed method.