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International Journal of Computer Mathematics Volume 94, 2017 - Issue 2
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Original Articles

A numerical approach for the Riesz space-fractional Fisher' equation in two-dimensions

Xiaogang ZhuDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi'an, ChinaView further author information
,
Yufeng NieDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi'an, ChinaCorrespondence[email protected]
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,
Jungang WangDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi'an, ChinaView further author information
&
Zhanbin YuanDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi'an, ChinaView further author information
Pages 296-315 | Received 10 May 2015, Accepted 01 Oct 2015, Published online: 19 Nov 2015

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Shuiping Yang. (2019) Numerical simulation for the two-dimensional and three-dimensional Riesz space fractional diffusion equations with delay and a nonlinear reaction term. International Journal of Computer Mathematics 96:10, pages 1957-1978.
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Articles from other publishers (27)

Alireza Ansari & Mohammad Hossein Derakhshan. (2024) Time–space fractional Euler–Poisson–Darboux equation with Bessel fractional derivative in infinite and finite domains. Mathematics and Computers in Simulation 218, pages 383-402.
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Jing Chen & Qi Wang. (2024) Numerical Stability and Convergence for Delay Space-Fractional Fisher Equations with Mixed Boundary Conditions in Two Dimensions. Communications on Applied Mathematics and Computation.
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Chetna Biswas, Subir Das, Anup Singh & Tomasz Sadowski. (2023) Numerical solution of two‐dimensional nonlinear Riesz space‐fractional reaction–advection–diffusion equation using fast compact implicit integration factor method. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 103:9.
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Wenwen Shan & Tao Wang. (2023) A two-level linearized scheme for two-dimensional Riesz space fractional nonlinear advection-dispersion equations. A two-level linearized scheme for two-dimensional Riesz space fractional nonlinear advection-dispersion equations.
Merfat Basha, Eyaya Fekadie Anley & Binxiang Dai. (2023) Linearized Crank–Nicolson Scheme for the Two-Dimensional Nonlinear Riesz Space-Fractional Convection–Diffusion Equation. Fractal and Fractional 7:3, pages 240.
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Pratibha Verma & Manoj Kumar. (2020) Existence and uniqueness results and analytical solution of the multi-dimensional Riesz space distributed-order advection–diffusion equation via two-step Adomian decomposition method. Engineering with Computers 38:3, pages 2051-2066.
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Xiaogang Zhu, Jimeng Li & Yaping Zhang. (2021) A local RBFs-based DQ approximation for Riesz fractional derivatives and its applications. Numerical Algorithms 90:1, pages 159-196.
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Huan-Yan Jian, Ting-Zhu Huang, Alexander Ostermann, Xian-Ming Gu & Yong-Liang Zhao. (2021) Fast IIF–WENO Method on Non-uniform Meshes for Nonlinear Space-Fractional Convection–Diffusion–Reaction Equations. Journal of Scientific Computing 89:1.
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M. Almushaira, H. Bhatt & A.M. Al-rassas. (2021) Fast high-order method for multi-dimensional space-fractional reaction–diffusion equations with general boundary conditions. Mathematics and Computers in Simulation 182, pages 235-258.
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X. G. Zhu, Y. F. Nie, J. G. Wang & Z. B. Yuan. (2021) An advanced meshless approach for the high-dimensional multi-term time-space-fractional PDEs on convex domains. Nonlinear Dynamics 104:2, pages 1555-1580.
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Huifang Yuan. (2021) An efficient spectral-Galerkin method for fractional reaction-diffusion equations in unbounded domains. Journal of Computational Physics 428, pages 110083.
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Pratibha Verma & Manoj Kumar. (2020) An analytical solution of multi-dimensional space fractional diffusion equations with variable coefficients. International Journal of Modeling, Simulation, and Scientific Computing 12:01, pages 2150006.
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Huan-Yan Jian, Ting-Zhu Huang, Xian-Ming Gu, Xi-Le Zhao & Yong-Liang Zhao. (2020) Fast implicit integration factor method for nonlinear space Riesz fractional reaction–diffusion equations. Journal of Computational and Applied Mathematics 378, pages 112935.
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Shuiping Yang, Fawang Liu, Libo Feng & Ian W. Turner. (2020) Efficient numerical methods for the nonlinear two-sided space-fractional diffusion equation with variable coefficients. Applied Numerical Mathematics 157, pages 55-68.
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Huan-Yan Jian, Ting-Zhu Huang, Xian-Ming Gu & Yong-Liang Zhao. (2020) Fast compact implicit integration factor method with non-uniform meshes for the two-dimensional nonlinear Riesz space-fractional reaction-diffusion equation. Applied Numerical Mathematics 156, pages 346-363.
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Huanyan Jian, Tingzhu Huang, Xianming Gu & Yongliang Zhao. (2020) Compact implicit integration factor method for two-dimensional space-fractional advection-diffusion-reaction equations. Journal of Physics: Conference Series 1592:1, pages 012048.
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M. Yousuf, K.M. Furati & A.Q.M. Khaliq. (2020) High-order time-stepping methods for two-dimensional Riesz fractional nonlinear reaction–diffusion equations. Computers & Mathematics with Applications 80:1, pages 204-226.
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X. G. Zhu, Y. F. Nie, Z. H. Ge, Z. B. Yuan & J. G. Wang. (2020) A class of RBFs-based DQ methods for the space-fractional diffusion equations on 3D irregular domains. Computational Mechanics 66:1, pages 221-238.
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Mahdi Saedshoar Heris, Mohammad Javidi & Bashir Ahmad. (2020) Stability and convergence of difference methods for two‐dimensional Riesz space fractional advection‐dispersion equations with delay. Computational and Mathematical Methods 2:3.
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Xiaogang Zhu, Yufeng Nie, Zhanbin Yuan, Jungang Wang & Zongze Yang. (2019) A Galerkin FEM for Riesz space-fractional CNLS. Advances in Difference Equations 2019:1.
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Xiujun Cheng, Jinqiao Duan & Dongfang Li. (2019) A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations. Applied Mathematics and Computation 346, pages 452-464.
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Baoli Yin, Yang Liu, Hong Li & Siriguleng He. (2019) Fast algorithm based on TT-M FE system for space fractional Allen–Cahn equations with smooth and non-smooth solutions. Journal of Computational Physics 379, pages 351-372.
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X. G. Zhu, Z. B. Yuan, F. Liu & Y. F. Nie. (2018) Differential quadrature method for space-fractional diffusion equations on 2D irregular domains. Numerical Algorithms 79:3, pages 853-877.
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Wenping Fan, Xiaoyun Jiang, Fawang Liu & Vo Anh. (2018) The Unstructured Mesh Finite Element Method for the Two-Dimensional Multi-term Time–Space Fractional Diffusion-Wave Equation on an Irregular Convex Domain. Journal of Scientific Computing 77:1, pages 27-52.
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Jingyuan Zhang. (2018) A stable explicitly solvable numerical method for the Riesz fractional advection–dispersion equations. Applied Mathematics and Computation 332, pages 209-227.
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Yang Liu, Zudeng Yu, Hong Li, Fawang Liu & Jinfeng Wang. (2018) Time two-mesh algorithm combined with finite element method for time fractional water wave model. International Journal of Heat and Mass Transfer 120, pages 1132-1145.
Crossref
X. G. Zhu, Y. F. Nie & W. W. Zhang. (2017) An efficient differential quadrature method for fractional advection–diffusion equation. Nonlinear Dynamics 90:3, pages 1807-1827.
Crossref

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