Computation of Hermite polynomials

Abstract

Abstract. Projection methods are commonly used to approximate solutions of ordinary and partial differential equations. A basis of the subspace under consideration is needed to apply the projection method. This paper discusses methods of obtaining a basis for piecewise polynomial Hermite subspaces. A simple recursive procedure is derived for generating piecewise Hermite polynomials. These polynomials are then used to obtain approximate solutions of differential equations.

On RHF and Bernoulli Polynomial for the numerical solution of differential equations

“…Thus, few numerical techniques were introduced to calculate approximate solutions for such equations. Such as Legendre polynomial [1], Chebyshev polynomial [2], Hermite polynomial [3,4], Bernoulli polynomial [5,6]. Recently, a new method developed to solve numerical problems by the concept of graph theory called Hosoya polynomial, one can refer for graph theory terminologies and developed method in [7,8,9,10,11,12,13].…”