An Efficient Finite Volume Method for Nonlinear Distributed-Order Space-Fractional Diffusion Equations in Three Space Dimensions

Xiangcheng Zheng; Huan Liu; Hong Wang; Hongfei Fu

doi:10.1007/s10915-019-00979-2

An Efficient Finite Volume Method for Nonlinear Distributed-Order Space-Fractional Diffusion Equations in Three Space Dimensions

Journal of Scientific Computing ◽

10.1007/s10915-019-00979-2 ◽

2019 ◽

Vol 80 (3) ◽

pp. 1395-1418 ◽

Cited By ~ 5

Author(s):

Xiangcheng Zheng ◽

Huan Liu ◽

Hong Wang ◽

Hongfei Fu

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Volume Method ◽

Three Space ◽

Distributed Order

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A fast finite volume method for conservative space-fractional diffusion equations in convex domains

Journal of Computational Physics ◽

10.1016/j.jcp.2016.01.015 ◽

2016 ◽

Vol 310 ◽

pp. 63-84 ◽

Cited By ~ 29

Author(s):

Jinhong Jia ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Convex Domains ◽

Fractional Diffusion Equations ◽

Volume Method

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Analysis and efficient implementation of alternating direction implicit finite volume method for Riesz space‐fractional diffusion equations in two space dimensions

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22554 ◽

2020 ◽

Vol 37 (1) ◽

pp. 818-835

Author(s):

Huan Liu ◽

Xiangcheng Zheng ◽

Hongfei Fu ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Riesz Space ◽

Diffusion Equations ◽

Alternating Direction Implicit ◽

Fractional Diffusion Equations ◽

Alternating Direction ◽

Two Space Dimensions ◽

Volume Method

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An efficient quadratic finite volume method for variable coefficient Riesz space‐fractional diffusion equations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6306 ◽

2020 ◽

Author(s):

Fangli Li ◽

Hongfei Fu ◽

Jun Liu

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Variable Coefficient ◽

Fractional Diffusion ◽

Riesz Space ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Volume Method

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A Parareal Finite Volume Method for Variable-Order Time-Fractional Diffusion Equations

Journal of Scientific Computing ◽

10.1007/s10915-020-01321-x ◽

2020 ◽

Vol 85 (1) ◽

Author(s):

Huan Liu ◽

Aijie Cheng ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Variable Order ◽

Fractional Diffusion Equations ◽

Volume Method

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A Fast Finite Volume Method on Locally Refined Meshes for Fractional Diffusion Equations

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.271118.280319 ◽

2019 ◽

Vol 9 (4) ◽

Cited By ~ 5

Author(s):

Jinhong Jia ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Refined Meshes ◽

Volume Method ◽

Locally Refined Meshes

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A finite volume method for two-sided fractional diffusion equations on non-uniform meshes

Journal of Computational Physics ◽

10.1016/j.jcp.2017.01.061 ◽

2017 ◽

Vol 335 ◽

pp. 747-759 ◽

Cited By ~ 16

Author(s):

Alex Simmons ◽

Qianqian Yang ◽

Timothy Moroney

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Volume Method

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Stability and convergence of a Crank–Nicolson finite volume method for space fractional diffusion equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.01.005 ◽

2019 ◽

Vol 139 ◽

pp. 38-51 ◽

Cited By ~ 6

Author(s):

Hongfei Fu ◽

Yanan Sun ◽

Hong Wang ◽

Xiangcheng Zheng

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Stability And Convergence ◽

Fractional Diffusion Equations ◽

Volume Method ◽

Crank Nicolson

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A fast finite volume method for conservative space–time fractional diffusion equations discretized on space–time locally refined meshes

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.04.003 ◽

2019 ◽

Vol 78 (5) ◽

pp. 1345-1356 ◽

Cited By ~ 6

Author(s):

Jinhong Jia ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Space Time ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Refined Meshes ◽

Volume Method ◽

Locally Refined Meshes

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Finite Volume Method for a Space Distributed-Order Time-Fractional Diffusion Equation

Pure Mathematics ◽

10.12677/pm.2019.93047 ◽

2019 ◽

Vol 09 (03) ◽

pp. 351-361

Author(s):

莹莹杨

Keyword(s):

Diffusion Equation ◽

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Fractional Diffusion Equation ◽

Volume Method ◽

Distributed Order

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Finite volume approximation with ADI scheme and low-rank solver for high dimensional spatial distributed-order fractional diffusion equations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.02.014 ◽

2021 ◽

Vol 89 ◽

pp. 116-126

Author(s):

Lot-Kei Chou ◽

Siu-Long Lei

Keyword(s):

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Low Rank ◽

High Dimensional ◽

Fractional Diffusion Equations ◽

Adi Scheme ◽

Volume Approximation ◽

Distributed Order ◽

Finite Volume Approximation

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