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International Journal of Computer Mathematics Volume 96, 2019 - Issue 2: A special collection of papers relating to or containing fractions
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Original Article

Crank–Nicolson Fourier spectral methods for the space fractional nonlinear Schrödinger equation and its parameter estimation

Hui ZhangSchool of Mathematics, Shandong University, Jinan, ChinaView further author information
,
Xiaoyun JiangSchool of Mathematics, Shandong University, Jinan, ChinaCorrespondence[email protected]
View further author information
,
Chu WangNokia Bell Labs, Murray Hill, NJ, USAView further author information
&
Shanzhen ChenSchool of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, ChinaView further author information
Pages 238-263 | Received 10 Sep 2017, Accepted 22 Jan 2018, Published online: 02 Mar 2018

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Mostafa Abbaszadeh & Mehdi Dehghan. (2021) Fourth-order alternating direction implicit difference scheme to simulate the space-time Riesz tempered fractional diffusion equation. International Journal of Computer Mathematics 98:11, pages 2137-2155.
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Articles from other publishers (18)

Jing Ning & Yu-Lan Wang. (2023) Fourier spectral method for solving fractional-in-space variable coefficient KdV-Burgers equation. Indian Journal of Physics 98:5, pages 1727-1744.
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Fengzhou Tian, Yulan Wang & Zhiyuan Li. (2024) Numerical Simulation of Soliton Propagation Behavior for the Fractional-in-Space NLSE with Variable Coefficients on Unbounded Domain. Fractal and Fractional 8:3, pages 163.
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Wei-Fang Tang, Yu-Lan Wang & Zhi-Yuan Li. (2023) Numerical simulation of fractal wave propagation of a multi-dimensional nonlinear fractional-in-space Schrödinger equation. Physica Scripta 98:4, pages 045205.
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Han Che, Yu-Lan Wang & Zhi-Yuan Li. (2022) Novel patterns in a class of fractional reaction–diffusion models with the Riesz fractional derivative. Mathematics and Computers in Simulation 202, pages 149-163.
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Jiale Tian, Ziyu Sun, Yang Liu & Hong Li. (2022) TT-M Finite Element Algorithm for the Coupled Schrödinger–Boussinesq Equations. Axioms 11:7, pages 314.
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Amin Khan, Muhammad Ahsan, Ebenezer Bonyah, Rashid Jan, Muhammad Nisar, Abdel-Haleem Abdel-Aty & Ibrahim S. Yahia. (2022) Numerical Solution of Schrödinger Equation by Crank–Nicolson Method. Mathematical Problems in Engineering 2022, pages 1-11.
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Yin Yang, Xueyang Li & Aiguo Xiao. (2021) Fourier pseudospectral method for fractional stationary Schrödinger equation. Applied Numerical Mathematics 165, pages 137-151.
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Nan Wang, Meng Li & Chengming Huang. (2021) Unconditional Energy Dissipation and Error Estimates of the SAV Fourier Spectral Method for Nonlinear Fractional Generalized Wave Equation. Journal of Scientific Computing 88:1.
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Xiaoqiang Yue, Kejia Pan, Jie Zhou, Zhifeng Weng, Shi Shu & Juan Tang. (2021) A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems. Computers & Mathematics with Applications 89, pages 57-67.
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Ahmed S. Hendy & Mahmoud A. Zaky. (2021) Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation. Nonlinear Dynamics 103:3, pages 2493-2507.
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Changhong Guo & Shaomei Fang. (2021) CRANK-NICOLSON DIFFERENCE SCHEME FOR THE DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION WITH THE RIESZ SPACE FRACTIONAL DERIVATIVE. Journal of Applied Analysis & Computation 11:3, pages 1074-1094.
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Mingfa Fei, Guoyu Zhang, Nan Wang & Chengming Huang. (2020) A linearized conservative Galerkin–Legendre spectral method for the strongly coupled nonlinear fractional Schrödinger equations. Advances in Difference Equations 2020:1.
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Nan Wang, Mingfa Fei, Chengming Huang, Guoyu Zhang & Meng Li. (2020) Dissipation-preserving Galerkin–Legendre spectral methods for two-dimensional fractional nonlinear wave equations. Computers & Mathematics with Applications 80:5, pages 617-635.
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Mingfa Fei, Nan Wang, Chengming Huang & Xiaohua Ma. (2020) A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation. Applied Numerical Mathematics 153, pages 399-411.
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Mingfa Fei, Chengming Huang & Pengde Wang. (2019) Error estimates of structure‐preserving Fourier pseudospectral methods for the fractional Schrödinger equation. Numerical Methods for Partial Differential Equations 36:2, pages 369-393.
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Xiu Yang, Xiaoyun Jiang & Hui Zhang. (2019) Finite difference spectral approximation for the time‐space fractional telegraph equation and its parameter estimation. Mathematical Methods in the Applied Sciences 42:18, pages 6475-6489.
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Chunlei Ruan. (2019) Chebyshev Spectral Collocation Method for Population Balance Equation in Crystallization. Mathematics 7:4, pages 317.
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Hui Zhang & Xiaoyun Jiang. (2018) Spectral method and Bayesian parameter estimation for the space fractional coupled nonlinear Schrödinger equations. Nonlinear Dynamics 95:2, pages 1599-1614.
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