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

Chun-Hua ZhangJun-Wei JinHai-Wei SunQin 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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