This paper deals with the construction of Schwarz Waveform Relaxation (SWR) methods for fractional diffusion-wave equations. SWR methods are a class of domain decomposition algorithms to solve evolution problems in parallel and have been mainly developed and analysed for several kinds of PDEs. We first analyse the convergence behaviour of the classical SWR method applied to fractional diffusion-wave equations, showing that Dirichlet boundary conditions at the artificial interfaces slow down the convergence of the method. Then, we construct optimal SWR methods, by providing the transmission conditions which assure convergence in two iterations.
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