In this paper, we presented some parallel diagonal implicit Runge-Kutta (PDIRK)iterative algorithms for a class of multistep Runge-Kutta methods presented by Butcherin 1960’s. Also in this paper we reached and proved...In this paper, we presented some parallel diagonal implicit Runge-Kutta (PDIRK)iterative algorithms for a class of multistep Runge-Kutta methods presented by Butcherin 1960’s. Also in this paper we reached and proved some conclusions on convergence,error estimation and stability of these algorithms. Numerical experiments showed thatthese algorithms are stable, convergent and error can be controlled if m (iteration times)is large enough.展开更多
This paper deals with the parallel diagonal implicit Runge-Kutta methods for solving DDEs with a constant delay. It is shown that the suitable choice of the predictor matrix can guarantee the stability of the methods....This paper deals with the parallel diagonal implicit Runge-Kutta methods for solving DDEs with a constant delay. It is shown that the suitable choice of the predictor matrix can guarantee the stability of the methods. It is proved that for the suitable selection of the diagonal matrix D, the method based on Radau IIA is δ-convergent, and the estimates for the non-stiff speed and the stiff speed of convergence are given.展开更多
文摘In this paper, we presented some parallel diagonal implicit Runge-Kutta (PDIRK)iterative algorithms for a class of multistep Runge-Kutta methods presented by Butcherin 1960’s. Also in this paper we reached and proved some conclusions on convergence,error estimation and stability of these algorithms. Numerical experiments showed thatthese algorithms are stable, convergent and error can be controlled if m (iteration times)is large enough.
文摘This paper deals with the parallel diagonal implicit Runge-Kutta methods for solving DDEs with a constant delay. It is shown that the suitable choice of the predictor matrix can guarantee the stability of the methods. It is proved that for the suitable selection of the diagonal matrix D, the method based on Radau IIA is δ-convergent, and the estimates for the non-stiff speed and the stiff speed of convergence are given.
