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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| Vydané v: | International journal of computer mathematics Ročník 100; číslo 7; s. 1419 - 1438 |
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| Jazyk: | English |
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Abingdon
Taylor & Francis
03.07.2023
Taylor & Francis Ltd |
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| Abstract | 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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| AbstractList | 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. 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. |
| Author | Mustafa, Almushaira |
| Author_xml | – sequence: 1 givenname: Almushaira surname: Mustafa fullname: Mustafa, Almushaira email: mstf1985@uestc.edu.cn organization: School of Mathematical Sciences/Institute of Computational Science, University of Electronic Science and Technology of China |
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| SubjectTerms | 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 |
| Title | A fast implicit difference scheme for solving high-dimensional time-space fractional nonlinear Schrödinger equation |
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