Convergence conditions on waveform relaxation of general differential-algebraic equations

Abstract

In the paper, we show some new convergence conditions on waveform relaxation (WR) for general differential-algebraic equations (DAEs). The main conclusion is that the convergence conditions on index r+1 can be derived from that of index r, in which the corresponding system is composed by ordinary differential equations if r=0. The approach of analysing relaxation process is novel for WR solutions of DAEs. It is also the first time to give the convergence conclusions for general index systems of DAEs in the WR field.

Keywords:

• differential-algebraic equations
• low or high index
• waveform relaxation
• convergence conditions
• engineering applications

2010 AMS Subject Classifications :

• 65L80
• 68W10
• 94C99

Acknowledgements

This research work was supported by the Natural Science Foundation of China NSFC10771168 and by the National Key Basic Research Program of China (973 program) under Grant 2005CB321701.