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

Xiaohua Ding & Mingzhu Liu

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 problem. 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.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-22-361, author = {Ding , Xiaohua and Liu , Mingzhu}, 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 problem. 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 AU - Ding , Xiaohua AU - Liu , Mingzhu 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, Parallel iteration, Delay differential equation. AB -

Implicit Runge-Kutta method is highly accurate and stable for stiff initial value problem. 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.

Ding , Xiaohua and Liu , Mingzhu. (2004). 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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