Partially explicit time discretization for time fractional diffusion equation

Time fractional PDEs have been used in many applications for modeling and simulations. Many of these are multiscale contain high contrast variations the media properties. It requires very small time step size to perform detailed computations. On other hand, presence spatial grids, is required explicit methods. Explicit methods advantages as we discuss paper. In this paper, propose a partial method PDEs. The approach solves forward problem on coarse computational grid, which much larger than heterogeneities, only few degrees freedom be treated implicitly. Via construction appropriate spaces careful stability analysis, can show that chosen not depend or scale mesh size. Thus, one use an approach. We present theory our proposed numerical results confirm findings demonstrate performance