Application of the hybrid functions to solve neutral delay functional differential equations

ABSTRACT

This paper presents a computational technique for the solution of the neutral delay differential equations with state-dependent and time-dependant delays. The properties of the hybrid functions which consist of block-pulse functions plus Legendre polynomials are presented. The approach uses these properties together with the collocation points to reduce the main problems to systems of nonlinear algebraic equations. An estimation of the error is given in the sense of Sobolev norms. The efficiency and accuracy of the proposed method are illustrated by several numerical examples.

KEYWORDS:

• neutral delay differential equation
• function approximation
• hybrid
• Legend repolynomials
• block–pulse functions

2010 AMS SUBJECT CLASSIFICATIONS:

• 41A10
• 65G99

Acknowledgement

The work of the third author was supported by Alzahra University.

Disclosure statement

No potential conflict of interest was reported by the authors.