A generalized-Jacobi-function spectral method for space-time fractional reaction-diffusion equations with viscosity terms

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.11.015 ◽

2020 ◽

Vol 152 ◽

pp. 355-378 ◽

Author(s):

Zhe Yu ◽

Boying Wu ◽

Jiebao Sun ◽

Wenjie Liu

Keyword(s):

Spectral Method ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Jacobi Function ◽

Fractional Reaction

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Solving linear and non-linear space-time fractional reaction-diffusion equations by the Adomian decomposition method

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.2165 ◽

2007 ◽

Vol 74 (1) ◽

pp. 138-158 ◽

Author(s):

Q. Yu ◽

F. Liu ◽

V. Anh ◽

I. Turner

Keyword(s):

Linear Space ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Adomian Decomposition ◽

Fractional Reaction

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Numerical Solution of Space-Time-Fractional Reaction-Diffusion Equations via the Caputo and Riesz Derivatives

Studies in Systems, Decision and Control - Mathematics Applied to Engineering, Modelling, and Social Issues ◽

10.1007/978-3-030-12232-4_5 ◽

2019 ◽

pp. 161-188 ◽

Author(s):

Kolade M. Owolabi ◽

Hemen Dutta

Keyword(s):

Numerical Solution ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Fractional Reaction

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A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations

Journal of Computational Physics ◽

10.1016/j.jcp.2019.109141 ◽

2020 ◽

Vol 405 ◽

pp. 109141 ◽

Author(s):

Hui Zhang ◽

Xiaoyun Jiang ◽

Fanhai Zeng ◽

George Em Karniadakis

Keyword(s):

Spectral Method ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Fourier Spectral Method ◽

Fractional Reaction

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Space-Time Fractional Reaction-Diffusion Equations Associated with a Generalized Riemann–Liouville Fractional Derivative

Axioms ◽

10.3390/axioms3030320 ◽

2014 ◽

Vol 3 (3) ◽

pp. 320-334 ◽

Author(s):

Ram Saxena ◽

Arak Mathai ◽

Hans Haubold

Keyword(s):

Fractional Derivative ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Liouville Fractional Derivative ◽

Fractional Reaction

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High-order time stepping Fourier spectral method for multi-dimensional space-fractional reaction–diffusion equations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2018.09.061 ◽

2019 ◽

Vol 77 (3) ◽

pp. 615-630 ◽

Author(s):

S.S. Alzahrani ◽

A.Q.M. Khaliq

Keyword(s):

Spectral Method ◽

Dimensional Space ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Fourier Spectral Method ◽

Time Stepping ◽

High Order Time ◽

Fractional Reaction

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Application Of Homotopy Perturbation Transform Method To Linear And Non-linear Space-time Fractional Reaction-diffusion Equations

Journal of Mathematics and Computer Science ◽

10.22436/jmcs.05.01.05 ◽

2012 ◽

Vol 05 (01) ◽

pp. 40-52 ◽

Author(s):

Jagdev Singh ◽

Devendra Kumar ◽

. ushila ◽

Sumit Gupta

Keyword(s):

Linear Space ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Transform Method ◽

Homotopy Perturbation ◽

Fractional Reaction

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Space-time finite element method for the distributed-order time fractional reaction diffusion equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.11.010 ◽

2020 ◽

Vol 152 ◽

pp. 446-465 ◽

Author(s):

Weiping Bu ◽

Lun Ji ◽

Yifa Tang ◽

Jie Zhou

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Distributed Order ◽

Fractional Reaction ◽

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Efficient Preconditioner Updates for Semilinear Space–Time Fractional Reaction–Diffusion Equations

Structured Matrices in Numerical Linear Algebra - Springer INdAM Series ◽

10.1007/978-3-030-04088-8_15 ◽

2019 ◽

pp. 285-302

Author(s):

Daniele Bertaccini ◽

Fabio Durastante

Keyword(s):

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Semilinear Space ◽

Fractional Reaction

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Fourier spectral method for higher order space fractional reaction–diffusion equations

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2016.04.020 ◽

2016 ◽

Vol 40 ◽

pp. 112-128 ◽

Author(s):

Edson Pindza ◽

Kolade M. Owolabi

Keyword(s):

Spectral Method ◽

Reaction Diffusion ◽

Higher Order ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Fourier Spectral Method ◽

Fractional Reaction

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Analytical Solution of Linear and Non-Linear Space-Time Fractional Reaction-Diffusion Equations

International Journal of Chemical Reactor Engineering ◽

10.2202/1542-6580.2359 ◽

2010 ◽

Vol 8 (1) ◽

Author(s):

Ahmet Yildirim ◽

Sefa A Sezer

Keyword(s):

Analytical Solution ◽

Linear Space ◽

Homotopy Perturbation Method ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Homotopy Perturbation ◽

Fractional Reaction

In this study, we present the homotopy perturbation method (HPM) for finding the analytical solution of linear and non-linear space-time fractional reaction-diffusion equations (STFRDE) on a finite domain. These equations are obtained from standard reaction-diffusion equations by replacing a second-order space deri-vative by a fractional derivative of order and a first-order time derivative by a fractional derivative of order. Some examples are given. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to linear and non-linear space-time fractional reaction-diffusion equations.

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