Numerical solution of the neutral functional-differential equations with proportional delays via collocation method based on Hermite polynomials

Abstract

In this paper, a collocation method based on Hermite polynomials is presented for the numerical solution of the neutral functional-differential equations (NFDEs) with proportional delays. By using Hermite polynomials and collocation points, NFDEs and the given conditions are transformed into matrix equation which corresponds to a system of linear algebraic equations with unknown Hermite coefficients. Hence, by solving this system, the unknown Hermite coefficients are computed. In addition, some numerical examples are given and comparisons with other methods are made in order to demonstrate the validity and applicability of the proposed method.