@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} }