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A spatially sixth-order hybrid $L 1$ -CCD method for solving time fractional Schrödinger equations

Chun-Hua Zhang; Jun-Wei Jin; Hai-Wei Sun; Qin Sheng — 2021

Applications of Mathematics

We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an $L 1$ 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 $L 1$ -CCD method is implemented successfully. The accuracy of this linearized scheme is order six in space, and order $2 - γ$ in time, where $0 < γ < 1$ is the order of the Caputo fractional derivative involved. It...

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