Residual correction of the Hermite polynomial solutions of the generalized pantograph equations

Abstract

In this paper, we consider the residual correction of the Hermite polynomial solutions of the generalized pantographequations. The Hermite polynomial solutions are obtained by a collocation method. By means of this collocation method, the problemis into a system of algebraic equations and thus unknown coefficients are determined. An error problem is constructed by using theorginal problem and the residual function. Error problem is solved by the Hermite collocation method and thus the imrovedapproximate solutions are gained. The technique is illustrated by studying the problem for two examples. The obtained results showthat the residual corrcetion method is very effective