Advertisement

The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1961–1973 | Cite as

Numerical method for two dimensional fractional reaction subdiffusion equation

  • H. Huang
  • X. CaoEmail author
Regular Article

Abstract

In this paper, a new numerical algorithm for solving two dimensional fractional reaction subdiffusion equation is proposed. The stability and convergency of this method are investigated by the Fourier analysis. Theoretical analysis and numerical experiment demonstrate that the proposed method is effective for solving the two dimensional fractional reaction subdiffusion equation.

Keywords

European Physical Journal Special Topic Fractional Derivative Convergence Analysis Fractional Calculus Fourier Series Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Hilfer, Applications of Fractional Calculus in Physics (World Scientific, 2000)Google Scholar
  2. 2.
    K.B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, 1974)Google Scholar
  3. 3.
    I. Podlubny, Fractional Differential Equations (Academic Press, 1999)Google Scholar
  4. 4.
    X. Cao, J. Fu, H. Huang, Adv. Appl. Math. Mech. 4, 848 (2012)MathSciNetzbMATHGoogle Scholar
  5. 5.
    C. Chen, F. Liu, I. Turner, V. Anh, J. Comp. Phys. 227, 886 (2007)MathSciNetADSCrossRefzbMATHGoogle Scholar
  6. 6.
    C. Chen, F. Liu, K. Burrage, Appl. Math. Comp. 198, 754 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    C. Chen, F. Liu, V. Anh, Numer. Algorithms 54, 1 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    C. Chen, F. Liu, V. Anh, I. Turner, Math. Comp. 81, 345 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    K. Diethelm, N.J. Ford, A.D. Freed, Numer. Agorithms 36, 31 (2004)MathSciNetADSCrossRefzbMATHGoogle Scholar
  10. 10.
    K. Diethelm, N.J. Ford, A.D. Freed, Yu. Luchko, Comput. Methods Appl. Mech. Engrg. 194, 743 (2005)MathSciNetADSCrossRefzbMATHGoogle Scholar
  11. 11.
    H. Ding, C. Li, J. Comp. Phys., doi:  10.1016/j.jcp.2013.02.014
  12. 12.
    C. Li, Z. Zhao, Y. Chen, Comput. Math. Appl. 62, 855 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    F. Liu, V. Anh, I. Turner, J. Comput. Appl. Math. 166, 209 (2004)MathSciNetADSCrossRefzbMATHGoogle Scholar
  14. 14.
    F. Liu, P. Zhuang, V. Anh, I. Turner, K. Burrage, Appl. Math. Comp. 191, 12 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    M. Meerschaert, C. Tadjeran, Comp. Appl. Math. 172, 65 (2004)MathSciNetADSCrossRefzbMATHGoogle Scholar
  16. 16.
    M. Meerschaert, H.P. Scheffler, C. Tadjeran, J. Comp. Phys. 211, 249 (2006)MathSciNetADSCrossRefzbMATHGoogle Scholar
  17. 17.
    J.P. Roop, Comp. Appl. Math. 193, 243 (2006)MathSciNetADSCrossRefzbMATHGoogle Scholar
  18. 18.
    I.M. Sokolov, J. Klafter, A. Blumen, Phys. Today 55, 48 (2002)CrossRefGoogle Scholar
  19. 19.
    E. Sousa, Comp. Math. Appl. 62, 938 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    E. Sousa, J. Comp. Phys. 228, 4038 (2009)MathSciNetADSCrossRefzbMATHGoogle Scholar
  21. 21.
    C. Tadjeran, M. Meerschaert, J. Comp. Phys. 220, 813 (2007)MathSciNetADSCrossRefzbMATHGoogle Scholar
  22. 22.
    S.B. Yuste, K. Lindenberg, Phys. Rev. Lett. 87, 118301 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    S.B. Yuste, K. Lindenberg, Chem. Phys. 284, 169 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    S.B. Yuste, L. Acedo, K. Lindenberg, Phys. Rev. E 69, 036126 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    S.B. Yuste, L. Acedo, SIAM J. Numer. Anal. 42, 1862 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    P. Zhuang, F. Liu, J. Appl. Math. Computing 25, 269 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityHunanChina

Personalised recommendations