THERMAL SCIENCE

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Yu-Yang Qiu

NUMERICAL APPROACH TO THE TIME-FRACTIONAL REACTION-DIFFUSION EQUATION

ABSTRACT
The numerical solution to the time-fractional reaction-diffusion equation with boundary conditions is considered in this paper. By difference, the problem is transformed to solve a linear system whose coefficient matrices are Toeplitz-like, and the solution can be constructed directly. Numerical results are reported to show the feasibility of the proposed method.
KEYWORDS
numerical solution, time-fractional reaction-diffusion equation, the linear equations, Toeplitz-like
PAPER SUBMITTED: 2018-03-07
PAPER REVISED: 2018-11-25
PAPER ACCEPTED: 2018-11-25
PUBLISHED ONLINE: 2019-09-14
DOI REFERENCE: https://doi.org/10.2298/TSCI1904245Q
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 4, PAGES [2245 - 2251]
REFERENCES
  1. Hashemi, M. S., et al., Lie Symmetry Analysis of Steady-State Fractional Reaction-Convection-Diffusion, Optik, 138 (2017), June, pp. 240-249
  2. Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific Press, Singapore, 2000
  3. Yang, X. J., Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher, Hong Kong, 2011
  4. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
  5. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, Elsevier, Amsterdam, The Netherlands, 2015
  6. Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
  7. Yu, Q., Liu, F. W., Implicit Difference Approximation for the Time-Fractional Order Reaction-Diffusion Equation, Journal of Xiamen University(Natural Science), 45 (2006), 3, pp. 315-319
  8. Liu, F., Anh, et al., Numerical Solution of the Space Fractional Fokker-Planck Equation, Journal of Computational and Applied Mathematics, 166 (2004), 1, pp. 209-219
  9. Wilkinson, J. H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, England, 1965
  10. Golub, G. H., Van Loan, C. F., Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, Md., USA, 1996
  11. Qiu, Y., Y., Solving a Class of Boundary Value Problems by LSQR, Thermal Science, 21 (2017), 4, pp. 1719-1724
  12. He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  13. Li, X. X., et al., A Fractal Modification of the Surface Coverage Model for an Electrochemical Arsenic Sensor, Electrochimica Acta, 296 (2019), Feb., pp. 491-493
  14. He, J.-H., Fractal Calculus and its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
  15. He, J.-H., et al., Geometrical Explanation of the Fractional Complex Transform and Derivative Chain Rule for Fractional Calculus, Phys. Lett. A, 376 (2012), 4, pp. 257-259
  16. Wang, Y., An, J. Y., Amplitude-Frequency Relationship to a Fractional Duffing Oscillator Arising in Microphysics and Tsunami Motion, Journal of Low Frequency Noise, Vibration & Active Control, On-line first, doi.org/10.1177/1461348418795813
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Numerical approach to the time-fractional reaction-diffusion equation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence