An approximation method for solving a neutral multi-pantograph equation and its convergence analysis

The main aim of this paper is to provide a numerical method for the solution of neutral multi pantograph equation. The method consists of expanding the required approximate solution as the elements of the shifted Legendre polynomials. The Legendre pantograph operational matrix is introduced. The operational matrices of pantograph, derivative and product are utilized to reduce the problem to a set of algebraic equations. We analyze the convergence properties of the present method to approximate solutions of the neutral multi pantograph equation.