Stability of implicit-explicit linear multistep methods for ordinary and delay differential equations
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- 作者：Toshiyuki Koto (1) koto@is.nagoya-u.ac.jp
- 关键词：Implicit ; explicit (IMEX) method ; delay differential equation ; stability region
- 刊名：Frontiers of Mathematics in China
- 出版时间：March 2009
- 出版年：2009
- 期刊代码：pc581_1673-3452
- 类别：mat
- 卷：4
- 期：1
- 页码：113-129
- 数据来源：sp
摘要
Stability properties of implicit-explicit (IMEX) linear multistep methods for ordinary and delay differential equations are analyzed on the basis of stability regions defined by using scalar test equations. The analysis is closely related to the stability analysis of the standard linear multistep methods for delay differential equations. A new second-order IMEX method which has approximately the same stability region as that of the IMEX Euler method, the simplest IMEX method of order 1, is proposed. Some numerical results are also presented which show superiority of the new method.