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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 2
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Original Articles

Unconditional error analysis of Galerkin FEMs for nonlinear fractional Schrödinger equation

Meng LiSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P.R. China.Correspondence[email protected]
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,
Chengming HuangSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P.R. China.View further author information
&
Zongbiao ZhangDepartment of Education, Bozhou University, Bozhou, P.R. China.View further author information
Pages 295-315 | Received 24 Jul 2016, Accepted 15 Nov 2016, Published online: 28 Nov 2016

Citations (16)

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Read on this site (2)

Wenping Fan & Xiaoyun Jiang. (2021) Error analysis of the unstructured mesh finite element method for the two-dimensional time-space fractional Schrödinger equation with a time-independent potential. International Journal of Computer Mathematics 98:8, pages 1663-1682.
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Fu-Rong Lin & Haidong Qu. (2019) A Runge–Kutta Gegenbauer spectral method for nonlinear fractional differential equations with Riesz fractional derivatives. International Journal of Computer Mathematics 96:2, pages 417-435.
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Articles from other publishers (14)

Zeting Liu, Baoli Yin & Yang Liu. (2023) An Explicit–Implicit Spectral Element Scheme for the Nonlinear Space Fractional Schrödinger Equation. Fractal and Fractional 7:9, pages 654.
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Fengli Yin, Dongliang Xu & Wenjie Yang. (2023) High-order schemes for the fractional coupled nonlinear Schrödinger equation. Networks and Heterogeneous Media 18:4, pages 1434-1453.
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Hongling Hu, Xianlin Jin, Dongdong He, Kejia Pan & Qifeng Zhang. (2021) A conservative difference scheme with optimal pointwise error estimates for two‐dimensional space fractional nonlinear Schrödinger equations. Numerical Methods for Partial Differential Equations 38:1, pages 4-32.
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Junjun Wang, Meng Li & Mengping Jiang. (2021) Superconvergence analysis of a MFEM for BBM equation with a stable scheme. Computers & Mathematics with Applications 93, pages 168-177.
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Lei Zhang, Rui Yang, Li Zhang & Lisha Wang. (2021) A Conservative Crank-Nicolson Fourier Spectral Method for the Space Fractional Schrödinger Equation with Wave Operators. Journal of Function Spaces 2021, pages 1-10.
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Junjun Wang. (2020) Superconvergence analysis of an energy stable scheme for nonlinear reaction-diffusion equation with BDF mixed FEM. Applied Numerical Mathematics 153, pages 457-472.
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Guang-an Zou, Bo Wang & Tony W.H. Sheu. (2020) On a conservative Fourier spectral Galerkin method for cubic nonlinear Schrödinger equation with fractional Laplacian. Mathematics and Computers in Simulation 168, pages 122-134.
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A. K. Mittal & L. K. Balyan. (2020) Chebyshev pseudospectral approximation of two dimensional fractional Schrodinger equation on a convex and rectangular domain. AIMS Mathematics 5:3, pages 1642-1662.
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Meng Li, Chengming Huang & Wanyuan Ming. (2019) A relaxation-type Galerkin FEM for nonlinear fractional Schrödinger equations. Numerical Algorithms 83:1, pages 99-124.
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Meng Li, Dongyang Shi, Junjun Wang & Wanyuan Ming. (2019) Unconditional superconvergence analysis of the conservative linearized Galerkin FEMs for nonlinear Klein-Gordon-Schrödinger equation. Applied Numerical Mathematics 142, pages 47-63.
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Wenping Fan & Haitao Qi. (2018) An efficient finite element method for the two-dimensional nonlinear time–space fractional Schrödinger equation on an irregular convex domain. Applied Mathematics Letters 86, pages 103-110.
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Meng Li, Chengming Huang & Wanyuan Ming. (2017) Mixed finite-element method for multi-term time-fractional diffusion and diffusion-wave equations. Computational and Applied Mathematics 37:2, pages 2309-2334.
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Guoyu Zhang, Chengming Huang & Meng Li. (2018) A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations. The European Physical Journal Plus 133:4.
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Meng Li, Xian-Ming Gu, Chengming Huang, Mingfa Fei & Guoyu Zhang. (2018) A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations. Journal of Computational Physics 358, pages 256-282.
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