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Numerical experiments display asymptotic consistency of the method when applied to simulated data . Using high-resolution SPH numerical simulations , we investigate the effects of gas on the inspiral and merger of binary black hole systems . Bars are complex systems and thanks to new observations and sophisticated numerical models developed in the last 20 years , considerable progress has been made in understanding their morphology , dynamics , formation and evolution . The linear stationary ones are the ones commonly derived in numerical analysis classes , but the subspace ones are generally more effective .