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International Journal of Computer Mathematics Volume 93, 2016 - Issue 10
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Original Articles

Fully discrete local discontinuous Galerkin methods for some time-fractional fourth-order problems

Li GuoDepartment of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, ChinaView further author information
,
Zhibo WangDepartment of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China;College of Mathematics and Statistics, Chongqing University, Chongqing401331, ChinaCorrespondence[email protected]
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&
Seakweng VongDepartment of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, ChinaView further author information
Pages 1665-1682 | Received 05 Jan 2015, Accepted 19 Jun 2015, Published online: 06 Aug 2015

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Zhen Wang. (2022) High-order numerical algorithms for the time-fractional convection–diffusion equation. International Journal of Computer Mathematics 99:11, pages 2327-2348.
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Changpin Li & Zhen Wang. (2021) Numerical Methods for the Time Fractional Convection-Diffusion-Reaction Equation. Numerical Functional Analysis and Optimization 42:10, pages 1115-1153.
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Wenlin Qiu, Da Xu & Hongbin Chen. (2020) A formally second-order BDF finite difference scheme for the integro-differential equations with the multi-term kernels. International Journal of Computer Mathematics 97:10, pages 2055-2073.
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Jafar Eshaghi, Hojatollah Adibi & Saeed Kazem. (2017) On a numerical investigation of the time fractional Fokker– Planck equation via local discontinuous Galerkin method. International Journal of Computer Mathematics 94:9, pages 1916-1942.
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Articles from other publishers (29)

Leilei Wei, Huanhuan Wang & Yanping Chen. (2023) Local discontinuous Galerkin method for a hidden-memory variable order reaction–diffusion equation. Journal of Applied Mathematics and Computing 69:3, pages 2857-2872.
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Hadi Mohammadi-Firouzjaei, Hojatollah Adibi & Mehdi Dehghan. (2023) Study of the backward difference and local discontinuous Galerkin (LDG) methods for solving fourth-order partial integro-differential equations (PIDEs) with memory terms: Stability analysis. Applied Numerical Mathematics 184, pages 567-580.
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Liuchao Xiao, Wenbo Li, Leilei Wei & Xindong Zhang. (2023) A fully discrete local discontinuous Galerkin method for variable-order fourth-order equation with Caputo-Fabrizio derivative based on generalized numerical fluxes. Networks and Heterogeneous Media 18:2, pages 532-546.
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Lijie Liu, Xiaojing Wei & Leilei Wei. (2023) A fully discrete local discontinuous Galerkin method based on generalized numerical fluxes to variable-order time-fractional reaction-diffusion problem with the Caputo fractional derivative. Electronic Research Archive 31:9, pages 5701-5715.
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Leilei Wei & Huanhuan Wang. (2023) Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation. Mathematics and Computers in Simulation 203, pages 685-698.
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Jing Guo, Qing Pan, Da Xu & Wenlin Qiu. (2022) A spectral order method for solving the nonlinear fourth-order time-fractional problem. Journal of Applied Mathematics and Computing 68:6, pages 4645-4667.
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Minghui Song, Jinfeng Wang, Yang Liu & Hong Li. (2022) Local discontinuous Galerkin method combined with the L2 formula for the time fractional Cable model. Journal of Applied Mathematics and Computing 68:6, pages 4457-4478.
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Farhad Fakhar-Izadi & Narges Shabgard. (2022) Time-space spectral Galerkin method for time-fractional fourth-order partial differential equations. Journal of Applied Mathematics and Computing 68:6, pages 4253-4272.
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Yuxuan Niu, Jinfeng Wang, Yang Liu, Hong Li & Zhichao Fang. (2022) Local discontinuous Galerkin method based on a family of second-order time approximation schemes for fractional mobile/immobile convection-diffusion equations. Applied Numerical Mathematics 179, pages 149-169.
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Zhen Wang. (2022) Numerical Analysis of Local Discontinuous Galerkin Method for the Time-Fractional Fourth-Order Equation with Initial Singularity. Fractal and Fractional 6:4, pages 206.
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Farhad Fakhar‐Izadi. (2020) Fully spectral‐Galerkin method for the one‐ and two‐dimensional fourth‐order time‐fractional partial integro‐differential equations with a weakly singular kernel. Numerical Methods for Partial Differential Equations 38:2, pages 160-176.
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Jinfeng Wang, Baoli Yin, Yang Liu, Hong Li & Zhichao Fang. (2021) A Mixed Element Algorithm Based on the Modified L1 Crank–Nicolson Scheme for a Nonlinear Fourth-Order Fractional Diffusion-Wave Model. Fractal and Fractional 5:4, pages 274.
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Leilei Wei & Wenbo Li. (2021) Local discontinuous Galerkin approximations to variable-order time-fractional diffusion model based on the Caputo–Fabrizio fractional derivative. Mathematics and Computers in Simulation 188, pages 280-290.
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Leilei Wei, Shuying Zhai & Xindong Zhang. (2020) Error Estimate of a Fully Discrete Local Discontinuous Galerkin Method for Variable-Order Time-Fractional Diffusion Equations. Communications on Applied Mathematics and Computation 3:3, pages 429-443.
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Changpin Li & Zhen Wang. (2021) Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution. Mathematics and Computers in Simulation 182, pages 838-857.
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Yanling Liu, Xuehua Yang, Haixiang Zhang & Yuan Liu. (2021) Analysis of BDF2 finite difference method for fourth-order integro-differential equation. Computational and Applied Mathematics 40:2.
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Leilei Wei & Yanfang Yang. (2021) Optimal order finite difference/local discontinuous Galerkin method for variable-order time-fractional diffusion equation. Journal of Computational and Applied Mathematics 383, pages 113129.
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Da Xu, Wenlin Qiu & Jing Guo. (2019) A compact finite difference scheme for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel. Numerical Methods for Partial Differential Equations 36:2, pages 439-458.
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Huiqin Zhang, Yan Mo & Zhibo Wang. (2020) A HIGH ORDER DIFFERENCE METHOD FOR FRACTIONAL SUB-DIFFUSION EQUATIONS WITH THE SPATIALLY VARIABLE COEFFICIENTS UNDER PERIODIC BOUNDARY CONDITIONS. Journal of Applied Analysis & Computation 10:2, pages 474-485.
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Xiaorui Sun, Can Li & Fengqun Zhao. (2020) Local discontinuous Galerkin methods for the time tempered fractional diffusion equation. Applied Mathematics and Computation 365, pages 124725.
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Jafar Eshaghi, Saeed Kazem & Hojjatollah Adibi. (2018) The local discontinuous Galerkin method for 2D nonlinear time-fractional advection–diffusion equations. Engineering with Computers 35:4, pages 1317-1332.
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Min Zhang, Yang Liu & Hong Li. (2019) High‐order local discontinuous Galerkin method for a fractal mobile/immobile transport equation with the Caputo–Fabrizio fractional derivative. Numerical Methods for Partial Differential Equations 35:4, pages 1588-1612.
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Changpin Li & Zhen Wang. (2019) The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: Numerical analysis. Applied Numerical Mathematics 140, pages 1-22.
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Xuhao Li & Patricia J. Y. Wong. (2018) An efficient numerical treatment of fourth-order fractional diffusion-wave problems. Numerical Methods for Partial Differential Equations 34:4, pages 1324-1347.
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Nan Liu, Yang Liu, Hong Li & Jinfeng Wang. (2018) Time second-order finite difference/finite element algorithm for nonlinear time-fractional diffusion problem with fourth-order derivative term. Computers & Mathematics with Applications 75:10, pages 3521-3536.
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Zhongsheng Yao & Zhibo Wang. (2018) A COMPACT DIFFERENCE SCHEME FOR FOURTH-ORDER FRACTIONAL SUB-DIFFUSION EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS. Journal of Applied Analysis & Computation 8:4, pages 1159-1169.
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Yanwei Du, Yang Liu, Hong Li, Zhichao Fang & Siriguleng He. (2017) Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation. Journal of Computational Physics 344, pages 108-126.
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Yang Liu, Min Zhang, Hong Li & Jichun Li. (2017) High-order local discontinuous Galerkin method combined with WSGD-approximation for a fractional subdiffusion equation. Computers & Mathematics with Applications 73:6, pages 1298-1314.
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Yajun Wang, Yang Liu, Hong Li & Jinfeng Wang. (2016) Finite element method combined with second-order time discrete scheme for nonlinear fractional Cable equation. The European Physical Journal Plus 131:3.
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