The Continuous Time Random Walk and the Finite Difference Method for the Space Time Fractional Diffusion Equations

Biostatistics and Biometrics Open Access Journal ◽

10.19080/bboaj.2017.03.555615 ◽

2017 ◽

Vol 3 (3) ◽

Author(s):

Abdel R E

Keyword(s):

Random Walk ◽

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Continuous Time ◽

Fractional Diffusion ◽

Continuous Time Random Walk ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

The Finite Difference Method

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A High Order Finite Difference Method for Tempered Fractional Diffusion Equations with Applications to the CGMY Model

SIAM Journal on Scientific Computing ◽

10.1137/18m1172739 ◽

2018 ◽

Vol 40 (5) ◽

pp. A3322-A3343 ◽

Author(s):

Xu Guo ◽

Yutian Li ◽

Hong Wang

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

High Order Finite Difference

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Finite difference method for time–space linear and nonlinear fractional diffusion equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2017.1344231 ◽

2017 ◽

Vol 95 (1) ◽

pp. 202-217 ◽

Author(s):

Sadia Arshad ◽

Weiping Bu ◽

Jianfei Huang ◽

Yifa Tang ◽

Yue Zhao

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Linear And Nonlinear

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A finite difference method with non-uniform timesteps for fractional diffusion equations

Computer Physics Communications ◽

10.1016/j.cpc.2012.07.011 ◽

2012 ◽

Vol 183 (12) ◽

pp. 2594-2600 ◽

Author(s):

Santos B. Yuste ◽

Joaquín Quintana-Murillo

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations

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A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.280218.210518 ◽

2018 ◽

Vol 8 (4) ◽

pp. 764-781

Author(s):

Sadia Arshad

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Fourth Order ◽

Difference Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

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A Fast Finite Difference Method for Three-Dimensional Time-Dependent Space-Fractional Diffusion Equations with Fractional Derivative Boundary Conditions

Journal of Scientific Computing ◽

10.1007/s10915-017-0478-8 ◽

2017 ◽

Vol 74 (2) ◽

pp. 1009-1033 ◽

Author(s):

Meng Zhao ◽

Hong Wang ◽

Aijie Cheng

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Boundary Conditions ◽

Fractional Derivative ◽

Difference Method ◽

Three Dimensional ◽

Fractional Diffusion ◽

Time Dependent ◽

Diffusion Equations ◽

Fractional Diffusion Equations

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A direct O(Nlog2N) finite difference method for fractional diffusion equations

Journal of Computational Physics ◽

10.1016/j.jcp.2010.07.011 ◽

2010 ◽

Vol 229 (21) ◽

pp. 8095-8104 ◽

Author(s):

Hong Wang ◽

Kaixin Wang ◽

Treena Sircar

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations

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Generalized finite difference method for a class of multidimensional space-fractional diffusion equations

Computational Mechanics ◽

10.1007/s00466-020-01917-y ◽

2020 ◽

Author(s):

Hong Guang Sun ◽

Zhaoyang Wang ◽

Jiayi Nie ◽

Yong Zhang ◽

Rui Xiao

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Multidimensional Space ◽

Fractional Diffusion Equations

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An O(N log2N) alternating-direction finite difference method for two-dimensional fractional diffusion equations

Journal of Computational Physics ◽

10.1016/j.jcp.2011.07.003 ◽

2011 ◽

Vol 230 (21) ◽

pp. 7830-7839 ◽

Author(s):

Hong Wang ◽

Kaixin Wang

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Two Dimensional ◽

Fractional Diffusion Equations ◽

Alternating Direction

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Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term

The Journal of Nonlinear Sciences and Applications ◽

10.22436/jnsa.011.01.03 ◽

2017 ◽

Vol 11 (01) ◽

pp. 17-25 ◽

Author(s):

Shuiping Yang

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Source Term ◽

Fractional Diffusion ◽

Riesz Space ◽

Diffusion Equations ◽

Nonlinear Source ◽

Fractional Diffusion Equations ◽

Equations With Delay

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From the space–time fractional integral of the continuous time random walk to the space–time fractional diffusion equations, a short proof and simulation

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2019.121547 ◽

2019 ◽

Vol 531 ◽

pp. 121547

Author(s):

E.A. Abdel-Rehim

Keyword(s):

Random Walk ◽

Continuous Time ◽

Fractional Integral ◽

Short Proof ◽

Fractional Diffusion ◽

Continuous Time Random Walk ◽

Diffusion Equations ◽

Fractional Diffusion Equations

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