An iterative splitting method via waveform relaxation

This paper explores a new numerical strategy for a closed formulation of iterative splitting methods and their embedding in classical waveform-relaxation methods. Since iterative splitting has been developed in several papers, an abstract framework that relates these methods to other classical splitting methods would be useful and is needed. Here, we present an embedding of the iterative splitting method in the waveform-relaxation and exponential splitting methods. While we can use the theoretical background of the classical schemes, a simpler iterative splitting analysis is obtained. This is achieved by basing the analysis on semigroup and fixpoint schemes. Our approach is illustrated with numerical results obtained on differential equations with constant and time-dependent coefficients.

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