Convergence of Parallel Diagonal Iteration of Runge-Kutta Methods for Delay Differential Equations

Convergence of Parallel Diagonal Iteration of Runge-Kutta Methods for Delay Differential Equations

Year:    2004

Author:    Xiaohua Ding, Mingzhu Liu

Journal of Computational Mathematics, Vol. 22 (2004), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2004-JCM-8856

Journal of Computational Mathematics, Vol. 22 (2004), Iss. 3 : pp. 361–370

Published online:    2004-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Runge-Kutta method Parallel iteration Delay differential equation.

Author Details

Xiaohua Ding

Mingzhu Liu