A new collocation method based on Euler polynomials for solution of generalized pantograph equations

Abstract

In this paper, a new collocation method based on Euler polynomials is improved for the numerical solution of generalized pantograph equations. This method transforms the generalized pantograph equations into the matrix equation with the help of Euler polynomials and collocation points. This matrix equation corresponds to a system of linear algebraic equations with the unknown Euler coefficients. By solving this system, the unknown Euler coefficients of the solution are found. Some numerical examples are given and comparisons with other methods are made in order to demonstrate the applicability and validity of the proposed method.