A Gauss Quadrature Like Numerical Integration Approach Based on Hermite Interpolation with Node Optimisation

Abstract

A numerical integration method based on Hermite interpolation is developed in this work. The basic idea is to use Hermite interpolation as the approximating agent for the integrand multiplied by a weight function. The nodes are chosen to suppress the error term of the Hermite interpolation. Even though this is a preliminary study, various important findings have been obtained. Some illustrative numerical implementations are also given.