Solving semi-linear stiff neutral equations by implicit–explicit Runge-Kutta methods

Abstract

In this paper, for solving semi-linear stiff neutral equations, a class of extended implicit–explicit Runge-Kutta (EIERK) methods are suggested. Under some suitable conditions, it is shown that an EIERK method is convergent of order one or two. The presented numerical examples further verify the theoretical results and effectiveness of the methods. A comparison with the adapted fully implicit Runge-Kutta methods shows that EIERK methods possess the higher computational efficiency.

Keywords:

• Implicit–explicit Runge-Kutta methods
• implicit Runge-Kutta methods
• stiff neutral equations
• error analysis
• computational efficiency

2010 Mathematics Subject Classifications:

• 65L03
• 65L04
• 65L05
• 65L06

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China (NSFC) (Grant No. 11971010.).