Volume 22, Issue 3
Convergence of Parallel Diagonal Iteration of Runge-Kutta Methods for Delay Differential Equations

Xiao-hua Ding & Mingzhu Liu

DOI:

J. Comp. Math., 22 (2004), pp. 361-370

Published online: 2004-06

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  • Abstract

Implicit Runge-Kutta method is highly accurate and stable for stiff initial value prob- lem. But the iteration technique used to solve implicit Runge-Kutta method requires lots of computational efforts. In this paper, we extend the Parallel Diagonal Iterated Runge- Kutta(PDIRK) methods to delay differential equations (DDEs). We give the convergence region of PDIRK methods, and analyze the speed of convergence in three parts for the P-stability region of the Runge-Kutta corrector method. Finally, we analysis the speed-up factor through a numerical experiment. The results show that the PDIRK methods to DDEs are efficient.

  • Keywords

Runge-Kutta method Parallel iteration Delay differential equation

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@Article{JCM-22-361, author = {}, title = {Convergence of Parallel Diagonal Iteration of Runge-Kutta Methods for Delay Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {3}, pages = {361--370}, abstract = { Implicit Runge-Kutta method is highly accurate and stable for stiff initial value prob- lem. But the iteration technique used to solve implicit Runge-Kutta method requires lots of computational efforts. In this paper, we extend the Parallel Diagonal Iterated Runge- Kutta(PDIRK) methods to delay differential equations (DDEs). We give the convergence region of PDIRK methods, and analyze the speed of convergence in three parts for the P-stability region of the Runge-Kutta corrector method. Finally, we analysis the speed-up factor through a numerical experiment. The results show that the PDIRK methods to DDEs are efficient. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8856.html} }
TY - JOUR T1 - Convergence of Parallel Diagonal Iteration of Runge-Kutta Methods for Delay Differential Equations JO - Journal of Computational Mathematics VL - 3 SP - 361 EP - 370 PY - 2004 DA - 2004/06 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8856.html KW - Runge-Kutta method KW - Parallel iteration KW - Delay differential equation AB - Implicit Runge-Kutta method is highly accurate and stable for stiff initial value prob- lem. But the iteration technique used to solve implicit Runge-Kutta method requires lots of computational efforts. In this paper, we extend the Parallel Diagonal Iterated Runge- Kutta(PDIRK) methods to delay differential equations (DDEs). We give the convergence region of PDIRK methods, and analyze the speed of convergence in three parts for the P-stability region of the Runge-Kutta corrector method. Finally, we analysis the speed-up factor through a numerical experiment. The results show that the PDIRK methods to DDEs are efficient.
Xiao-hua Ding & Mingzhu Liu . (1970). Convergence of Parallel Diagonal Iteration of Runge-Kutta Methods for Delay Differential Equations. Journal of Computational Mathematics. 22 (3). 361-370. doi:
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