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In this talk,we will present some waveform relaxation (WR) methods for differential algebraic equations (DAEs) and partial differential equations (PDEs).We will give a new convergence strategy for systems of DAEs of high index.Meanwhile,Schwarz waveform relaxation (SWR) methods based on different transmission conditions are considered to solve time-periodic PDEs.Here,we will present a proof on convergence of the overlapping SWR in energy norm for the case of the heat equation,in contrast with the previous analysis based on the maximum principle given in maximum norm.