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 - <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>