| Abstract: |
| We consider the numerical solution to two types of fractional partial differential equations, i.e. time fractional wave problems and modified anomalous subdiffusion problems. For the time fractional wave problems, we develop a high-accuracy algorithm which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. For the modified anomalous subdiffusion problems with two time fractional derivatives of orders $ \alpha $ and $ \beta $ ($ 0 < \alpha < \beta < 1 $), we use a time-stepping
discontinuous Galerkin method in the temporal discretization and a finite element method in the spatial discretization. Stability and convergence of the algorithms are derived. Numerical experiments are provided to verify the theoretical results. |
|