Operational method for the solution of ordinary differential equations using Hermite series

Abstract

We apply a general algebraic operational method to obtain solutions of ordinary differential equations.  The solutions are expressed as series of scaled  Hermite  polynomials.  We present some examples that show that the solutions obtained as truncated Hermite series give acceptable approximations to the exact solutions on intervals larger than the corresponding intervals for the solutions obtained as truncated Taylor series.  Our method is algebraic and doesn't use any integral transforms.