A spatially sixth-order hybrid $L1$-CCD method for solving time fractional Schrödinger equations
- Zhang, Chun-Hua
- Jin, Jun-Wei
- Sun, Hai-Wei
- Sheng, Qin
DOIAbstract
summary:We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an $L1$ strategy is employed for approximating the Caputo fractional derivative in the temporal direction, compact CCD finite difference approaches are incorporated in the space. A highly effective hybrid $L1$-CCD method is implemented successfully. The accuracy of this linearized scheme is order six in space, and order $2-\gamma $ in time, where $0<\gamma <1$ is the order of the Caputo fractional derivative involved. It is proved rigorously that the hybrid numerical method accomplished is unconditionally stable in the Fourier sense. Numerical experiments are carried out with typical testing problems to validate the effectiveness ...
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