An analysis of convergence for nonstationary two-stage multisplitting waveform relaxation methods

Abstract

In this paper, we consider a nonstationary multisplitting two-stage strategy for waveform relaxation iterations, solving the initial value problem of ordinary differential equations. Convergence properties will be given when the coefficient matrix is an M-matrix or a Hermitian positive definite matrix. Finally numerical experiments are presented.

In Memory of Professor D.J. Evans

Keywords:

• Nonstationary
• Relaxed stationary
• Waveform relaxation
• M-splitting
• Hermitian P-regular

Acknowledgements

The authors would like to thank the referees for their helpful comments and suggestions that significantly improved this paper, and Laura Northover for her help in publishing the paper. Supported by the NCET in universities of China (NCET-04-0893), scientific and technological key project of the Chinese Ministry of Education (107098) and project of academic leader and group of UESTC.

Notes

In Memory of Professor D.J. Evans