Numerical solution of functional differential equations: a Green's function-based iterative approach

ABSTRACT

In this article, a recently introduced iterative method based on Green's functions and fixed-point iteration schemes is presented for the approximate solutions of delay and functional differential equations. The approach is especially suited for handling boundary value problems (BVPs). The algorithm is illustrated through a number of examples that confirm the high accuracy and efficiency of the strategy. The results of the test examples show excellent agreement with exact solutions and outperforms other existing numerical iterative schemes.

KEYWORDS:

• Functional differential equations
• delay differential equations
• Green's function
• fixed point iterative schemes

2010 AMS SUBJECT CLASSIFICATIONS:

• 65Qxx
• 39A
• 39B

Disclosure statement

No potential conflict of interest was reported by the authors.