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.