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A multidomain spectral method with compactified exterior domains combined with stable second and fourth order time integrators is presented for Schr(o)dinger equations.The numerical approach allows high precision numerical studies of solutions on the whole real line.At examples for the linear and cubic nonlinear Schr(o)dinger equation,this code is compared to transparent boundary conditions and perfectly matched layers approaches.The code can deal with asymptotically non vanishing solutions as the Peregrine breather being discussed as a model for rogue waves.