Stability and convergence analysis of implicit–explicit one-leg methods for stiff delay differential equations

Abstract

The purpose of this paper is devoted to studying the implicit–explicit (IMEX) one-leg methods for stiff delay differential equations (DDEs) which can be split into the stiff and nonstiff parts. IMEX one-leg methods are composed of implicit one-leg methods for the stiff part and explicit one-leg methods for the nonstiff part. We prove that if the IMEX one-leg methods is consistent of order 2 for the ordinary differential equations, and the implicit one-leg method is A-stable, then the IMEX one-leg methods for stiff DDEs are stable and convergent with order 2. Some numerical examples are given to verify the validity of the obtained theoretical results and the effectiveness of the presented methods.

Keywords:

• stiff delay differential equations
• implicit–explicit one-leg methods
• convergence
• stability

2010 AMS Subject Classifications:

• 65L04
• 65L03
• 65L06
• 65L20

Acknowledgments

We are indebted to the reviewers for the useful comments and valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (Grant No.11271311), the Research Foundation of Education Commission of Hunan Province of China (Grant No. 14A146) and Hunan Province Innovation Foundation for Postgraduate (Grant No. CX2014B253).