A fast implicit difference scheme for solving high-dimensional time-space fractional nonlinear Schrödinger equation

In this work, an efficient implicit difference scheme is developed for solving the high-dimensional time-space fractional nonlinear Schrödinger equation. The derived scheme is constructed by utilizing a fast evaluation of Caputo fractional derivative based on the - formula; meanwhile, the compact fi...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 100; no. 7; pp. 1419 - 1438
Main Author: Mustafa, Almushaira
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.07.2023
Taylor & Francis Ltd
Subjects:
Error analysis
fast algorithm
Finite difference method
Iterative algorithms
Iterative methods
matrix transfer technique
Nonlinear systems
Schrodinger equation
stability
Stability analysis
Time-space fractional Schrödinger equation
Truncation errors
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:In this work, an efficient implicit difference scheme is developed for solving the high-dimensional time-space fractional nonlinear Schrödinger equation. The derived scheme is constructed by utilizing a fast evaluation of Caputo fractional derivative based on the - formula; meanwhile, the compact finite difference with matrix transfer technique is adopted for the spatial discretization. Moreover, a linearized iteration method based on the fast discrete sine transform technique is considered to solve the nonlinear system effectively. Because the resultant algorithm does not use matrix inversion, it is computationally efficient in long-time calculations. The stability, truncation error and convergence analysis of the discrete scheme are discussed in detail. Furthermore, a fast iterative algorithm is provided. Finally, several numerical examples are given to verify the efficiency and accuracy of the derived scheme, and a comparison with similar work is presented.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2023.2190422