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Research Article

A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation

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Pages 1877-1895 | Received 05 Dec 2022, Accepted 28 May 2023, Published online: 30 Jun 2023
 

Abstract

The fractional Schrödinger equation is an important fractional nonlinear evolution equation, and the study of its numerical solution has profound scientific meaning and wide application prospects. This paper proposes a new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation (TFSE). The Caputo time-fractional derivative is discretized by high-order L21σ formula and the fourth-order compact difference approximation is applied for spatial discretization. A new nonlinear compact difference scheme with temporal second-order and spatial fourth-order accuracy is constructed, which is solved by the efficient linearized iterative algorithm. The unconditional stability and convergence are analysed by the energy method. The unique existence and maximum-norm estimate of new compact difference scheme solution are obtained. Theoretical analysis shows that the convergence accuracy of new compact difference scheme is O(τ2+h4) with the strong regularity assumption. Numerical experiments verify theoretical results and indicate that the proposed method is an efficient numerical method for solving TFSE.

2020 Mathematics Subject Classifications:

Acknowledgments

The authors express the sincere gratitude to Dr. Lifei Wu and Dr. Xinlong Liu (North China Electric Power University) for their effective advice.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (Grant No. 11371135).

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