A New Hermite Collocation Method for Solving Differential Difference Equations

Abstract

The purpose of this study is to give a Hermite polynomial approximation for the solution of m(th) order linear differential-difference equations with variable coefficients under mixed conditions. For this purpose, a new Hermite collocation method is introduced. This method is based on the truncated Hermite expansion of the function in the differential-difference equations. Hence, the resulting matrix equation can be solved and the unknown Hermite coefficients can be found approximately. In addition, examples that illustrate the pertinent features of the method are presented and the results of the study discussed.