Convergence of Parallel Diagonal Iteration of Runge-Kutta Methods for Delay Differential Equations
Xiao Hua Ding 1, Ming Zhu Liu 11 Department of Mathematics, Harbin Institute of Technology (Wcihai), Wcihai 264209, China
Implicit Runge-Kutta method is highly accurate and stable for stiff initial value prob- lem. 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.
Key words: Runge-Kutta method; Parallel iteration; Delay differential equation.