article

Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

Authors:

K. BurrageAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 231, Issue 1

Pages 160 - 176

https://doi.org/10.1016/j.cam.2009.02.013

Published: 01 September 2009 Publication History

Abstract

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis.

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cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 231, Issue 1

September, 2009

491 pages

ISSN:0377-0427

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Copyright © Elsevier B.V. © 2009.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 September 2009

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Cited By

Ngondiep E(2023)A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivativeNumerical Algorithms10.1007/s11075-023-01516-x94:2(681-700)Online publication date: 4-Mar-2023
https://dl.acm.org/doi/10.1007/s11075-023-01516-x
Zhang GHuang CAlikhanov AYin B(2023)A High-Order Discrete Energy Decay and Maximum-Principle Preserving Scheme for Time Fractional Allen–Cahn EquationJournal of Scientific Computing10.1007/s10915-023-02263-w96:2Online publication date: 15-Jun-2023
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Bhatt HKhaliq AFurati K(2020)Efficient high-order compact exponential time differencing method for space-fractional reaction-diffusion systems with nonhomogeneous boundary conditionsNumerical Algorithms10.1007/s11075-019-00729-383:4(1373-1397)Online publication date: 1-Apr-2020
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Zhu L(2019)A Second-Order Uniformly Stable Explicit Asymmetric Discretization Method for One-Dimensional Fractional Diffusion EquationsComplexity10.1155/2019/42384202019Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1155/2019/4238420
Chen YChen C(2018)Numerical simulation with the second order compact approximation of first order derivative for the modified fractional diffusion equationApplied Mathematics and Computation10.1016/j.amc.2017.07.070320:C(319-330)Online publication date: 1-Mar-2018
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Abu Arqub O(2017)Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditionsComputers & Mathematics with Applications10.1016/j.camwa.2016.11.03273:6(1243-1261)Online publication date: 15-Mar-2017
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Cao XCao XWen L(2017)The implicit midpoint method for the modified anomalous sub-diffusion equation with a nonlinear source termJournal of Computational and Applied Mathematics10.1016/j.cam.2016.10.014318:C(199-210)Online publication date: 1-Jul-2017
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Zhang PPu H(2017)A second-order compact difference scheme for the fourth-order fractional sub-diffusion equationNumerical Algorithms10.1007/s11075-017-0271-776:2(573-598)Online publication date: 1-Oct-2017
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