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In this paper, we take the equation ut = uxx for example, and give a practical difference scheme with intrinsic parallelism, which is based on an implicit scheme inside boundary layers and an explicit scheme on them. At the same time, the supper-time-stepping algorithm is presented. It can significantly increase the performance of the difference scheme with intrinsic parallelism by reducing the restrictive timestep limits that exist. It is obviously that this scheme is advantageous to parallel computing. We prove its stability, and also give its results of numerical experiments.
In this paper, we take the equation ut = uxx for example, and give a practical difference scheme with intrinsic parallelism, which is based on an implicit scheme inside boundary layers and an explicit scheme on them. At the same time, the supper-time It can obviously increase the performance of the difference scheme with intrinsic parallelism by reducing the restrictive timestep that that exist. It is that that scheme is advantageous to parallel computing. We prove its stability, and also give its results of numerical experiments.