Abstract. Computer simulations of decoherence in quantum spin systems require the solution of the time-dependent Schrödinger equation for interacting quantum spin systems over extended periods of time. We use exact diagonalization, Chebyshev polynomial technique, four Suzukiformula algorithms, and the short-iterative-Lanczos method to solve a simple model for decoherence of a quantum spin system by an environment consisting of quantum spins, and compare advantages and limitations of different algorithms. 1