Chaotic waveform relaxation methods for dynamical systems

摘要

For solving the large dynamical systems of initial value problems that can be described by a system of mixed implicit differential equations, the waveform relaxation (WR) methods are proposed and investigated by some mathematicians. In this paper, in order to compute the WR methods on parallel processors and to avoid the synchronization costs, the chaotic waveform relaxation (WR) methods are presented and their convergence is investigated. As for the special cases, the nonlinear ODEs, linear ODEs and semi-explicit DAEs are discussed, respectively.