  In this paper we investigate a sub-diffusion equation for simulating the
anomalous diffusion phenomenon in real physical environment. Based on an
equivalent transformation of the original sub-diffusion equation followed by
the use of a smooth operator, we devise a high-order numerical scheme by
combining the Nystrom method in temporal direction with the compact finite
difference method and the spectral method in spatial direction. The distinct
advantage of this approach in comparison with most current methods is its high
convergence rate even though the solution of the anomalous sub-diffusion
equation usually has lower regularity on the starting point. The effectiveness
and efficiency of our proposed method are verified by several numerical
experiments.
