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International Journal of Computer Mathematics Volume 93, 2016 - Issue 3
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Articles

Finite difference schemes for two-dimensional time-space fractional differential equations

Zhibo WangDepartment of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, ChinaCorrespondence[email protected]
,
Seakweng VongDepartment of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China
&
Siu-Long LeiDepartment of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China
Pages 578-595 | Received 01 Jul 2014, Accepted 01 Jan 2015, Published online: 10 Feb 2015

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J. E. Macías-Díaz. (2019) On the solution of a Riesz space-fractional nonlinear wave equation through an efficient and energy-invariant scheme. International Journal of Computer Mathematics 96:2, pages 337-361.
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Articles from other publishers (16)

Yun-Chi Huang, Lot-Kei Chou & Siu-Long Lei. (2023) Divide-and-Conquer Solver in Tensor-Train Format for d-Dimensional Time-Space Fractional Diffusion Equations. Journal of Scientific Computing 96:1.
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Victor N. Orlov, Asmaa M. Elsayed & Elsayed I. Mahmoud. (2022) Two Linearized Schemes for One-Dimensional Time and Space Fractional Differential Equations. Mathematics 10:19, pages 3651.
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Emadidin Gahalla Mohmed Elmahdi & Jianfei Huang. (2022) EFFICIENT NUMERICAL SOLUTION OF TWO-DIMENSIONAL TIME-SPACE FRACTIONAL NONLINEAR DIFFUSION-WAVE EQUATIONS WITH INITIAL SINGULARITY. Journal of Applied Analysis & Computation 12:2, pages 831-849.
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Jianfei Huang, Zhi Qiao, Jingna Zhang, Sadia Arshad & Yifa Tang. (2020) Two linearized schemes for time fractional nonlinear wave equations with fourth-order derivative. Journal of Applied Mathematics and Computing 66:1-2, pages 561-579.
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Bingqing Lu, Xiaoting Liu, Peiyao Dong, Geoffrey R. Tick, Chunmiao Zheng, Yong Zhang, Muhammad Mahmood-UI-Hassan, Hongjuan Bai & Edvina Lamy. (2020) Quantifying fate and transport of nitrate in saturated soil systems using fractional derivative model. Applied Mathematical Modelling 81, pages 279-295.
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Xue-Lei Lin & Michael K. Ng. (2019) A fast solver for multidimensional time–space fractional diffusion equation with variable coefficients. Computers & Mathematics with Applications 78:5, pages 1477-1489.
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Shuying Zhai, Zhifeng Weng, Xinlong Feng & Jinyun Yuan. (2018) Investigations on several high-order ADI methods for time-space fractional diffusion equation. Numerical Algorithms 82:1, pages 69-106.
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Lot-Kei Chou & Siu-Long Lei. (2019) Tensor-Train Format Solution with Preconditioned Iterative Method for High Dimensional Time-Dependent Space-Fractional Diffusion Equations with Error Analysis. Journal of Scientific Computing 80:3, pages 1731-1763.
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Seakweng Vong & Pin Lyu. (2019) On a second order scheme for space fractional diffusion equations with variable coefficients. Applied Numerical Mathematics 137, pages 34-48.
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Seakweng Vong, Chenyang Shi & Pin Lyu. (2019) A study on a second order finite difference scheme for fractional advection-diffusion equations. Numerical Methods for Partial Differential Equations 35:2, pages 493-508.
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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.
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Sadia Arshad, Jianfei Huang, Abdul Q.M. Khaliq & Yifa Tang. (2017) Trapezoidal scheme for time–space fractional diffusion equation with Riesz derivative. Journal of Computational Physics 350, pages 1-15.
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Yun-Chi Huang & Siu-Long Lei. (2017) A fast numerical method for block lower triangular Toeplitz with dense Toeplitz blocks system with applications to time-space fractional diffusion equations. Numerical Algorithms 76:3, pages 605-616.
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Lot-Kei Chou & Siu-Long Lei. (2017) Fast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy. Computers & Mathematics with Applications 73:3, pages 385-403.
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Siu-Long Lei, Xu Chen & Xinhe Zhang. (2016) Multilevel Circulant Preconditioner for High-Dimensional Fractional Diffusion Equations. East Asian Journal on Applied Mathematics 6:2, pages 109-130.
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Seakweng Vong, Pin Lyu, Xu Chen & Siu-Long Lei. (2015) High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives. Numerical Algorithms 72:1, pages 195-210.
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