Partially explicit time discretization for nonlinear time fractional diffusion equations

Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there high contrast changes media properties. For solving these problems, one often uses coarse spatial grid for resolution. temporal discretization, implicit methods used. methods, though the step can be relatively large, difficult to compute due nonlinearity fact that deals with large-scale systems. On other hand, discrete system explicit easier but it requires small steps. this work, we propose partially scheme following earlier works on developing nonlinear diffusion equations. scheme, term is treated explicitly reaction fully explicitly. With appropriate construction of spaces stability analysis, find required our proposed scales as mesh size, which creates a great saving computing. The main novelty work extension case equations, constraints steps more severe alleviate since method size. We present results. Numerical results presented where compare approach. show approach provides similar results, while treating degrees freedom terms