@Article{JCM-22-3,
author = {Xiaohua, Ding and Mingzhu, Liu},
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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/2004-JCM-8856},
url = {https://global-sci.com/article/85225/convergence-of-parallel-diagonal-iteration-of-runge-kutta-methods-for-delay-differential-equations}
}