Convergence Aspects of Step-Parallel Iteration of Runge-Kutta Methods for Delay Differential Equations
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- 作者：Xiaohua Ding and Mingzhu Liu
- 关键词：Runge ; Kutta method ; step ; parallel iteration ; delay differential equation
- 刊名：BIT Numerical Mathematics
- 出版时间：September 2002
- 出版年：2002
- 期刊代码：30_0006-3835
- 类别：mat
- 卷：42
- 期：3
- 页码：508-518
- 数据来源：sp
摘要
Implicit Runge-Kutta methods are known as highly accurate and stable methods for solving differential equations. However, the iteration technique used to solve implicit Runge-Kutta methods requires a lot of computational efforts. To lessen the computational effort, one can iterate simultaneously at a number of points along the t-axis. In this paper, we extend the PDIRK (Parallel Diagonal Iterated Runge-Kutta) methods to delay differential equations (DDEs). We give the region of convergence and analyze the speed of convergence in three parts for the P-stability region of the Runge-Kutta corrector. It is proved that PDIRK methods to DDEs are efficient, and the diagonal matrix D of the PDIRK methods for DDES can be selected in the same way as for ordinary differential equations (ODEs).