Sequential and parallel Rosenbrock methods for delay differential equations

Xuenian Cao, Shoufu Li

Department of Mathematics, Xiangtan University, Xiangtan 411105, P.R. China

cxn@xtu.edu.cn

Contributed talk

Runge-Kutta methods and $\theta$-methods in the numerical solution of delay differential equations have been deeply studied. In this paper a class of Rosenbrock methods for solving delay differential equations is constructed by making some modification about a class of Rosenbrock methods for solving ordinary differential equations. It is proved that these methods are GP-stable. On this basis a class of parallel Rosenbrock methods for solving delay differential equations is constructed. Numerical experiments show that the sequential and parallel Rosenbrock methods are efficient for solving delay differential equations.