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A spatially sixth-order hybrid \(L1\)-CCD method for solving time fractional Schrödinger equations. (English) Zbl 07332696

In this paper, highly accurate schemes for nonlinear time fractional Schrödinger equations are considered. The paper is organized as follows. Section 1 is an introduction. In Section 2, the linearized and spatially sixth-order combined compact difference strategy is introduced and studied. The stability analysis is given in Section 3. Computational experiments with typical testing problems to validate the effectiveness of the algorithms are presented in Section 4. Finally, brief remarks and conclusions are given in Section 5.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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