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Numerical method for two dimensional fractional reaction subdiffusion equation

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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.

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References

  1. R. Hilfer, Applications of Fractional Calculus in Physics (World Scientific, 2000)

  2. K.B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, 1974)

  3. I. Podlubny, Fractional Differential Equations (Academic Press, 1999)

  4. X. Cao, J. Fu, H. Huang, Adv. Appl. Math. Mech. 4, 848 (2012)

    MathSciNet  MATH  Google Scholar 

  5. C. Chen, F. Liu, I. Turner, V. Anh, J. Comp. Phys. 227, 886 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. C. Chen, F. Liu, K. Burrage, Appl. Math. Comp. 198, 754 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. C. Chen, F. Liu, V. Anh, Numer. Algorithms 54, 1 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. C. Chen, F. Liu, V. Anh, I. Turner, Math. Comp. 81, 345 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. K. Diethelm, N.J. Ford, A.D. Freed, Numer. Agorithms 36, 31 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. K. Diethelm, N.J. Ford, A.D. Freed, Yu. Luchko, Comput. Methods Appl. Mech. Engrg. 194, 743 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. H. Ding, C. Li, J. Comp. Phys., doi: 10.1016/j.jcp.2013.02.014

  12. C. Li, Z. Zhao, Y. Chen, Comput. Math. Appl. 62, 855 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Liu, V. Anh, I. Turner, J. Comput. Appl. Math. 166, 209 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. F. Liu, P. Zhuang, V. Anh, I. Turner, K. Burrage, Appl. Math. Comp. 191, 12 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. M. Meerschaert, C. Tadjeran, Comp. Appl. Math. 172, 65 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. M. Meerschaert, H.P. Scheffler, C. Tadjeran, J. Comp. Phys. 211, 249 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. J.P. Roop, Comp. Appl. Math. 193, 243 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. I.M. Sokolov, J. Klafter, A. Blumen, Phys. Today 55, 48 (2002)

    Article  Google Scholar 

  19. E. Sousa, Comp. Math. Appl. 62, 938 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. E. Sousa, J. Comp. Phys. 228, 4038 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. C. Tadjeran, M. Meerschaert, J. Comp. Phys. 220, 813 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. S.B. Yuste, K. Lindenberg, Phys. Rev. Lett. 87, 118301 (2001)

    Article  ADS  Google Scholar 

  23. S.B. Yuste, K. Lindenberg, Chem. Phys. 284, 169 (2002)

    Article  ADS  Google Scholar 

  24. S.B. Yuste, L. Acedo, K. Lindenberg, Phys. Rev. E 69, 036126 (2004)

    Article  ADS  Google Scholar 

  25. S.B. Yuste, L. Acedo, SIAM J. Numer. Anal. 42, 1862 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  26. P. Zhuang, F. Liu, J. Appl. Math. Computing 25, 269 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan, 411105, China

    H. Huang & X. Cao

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  1. H. Huang
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  2. X. Cao
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Correspondence to X. Cao.

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Huang, H., Cao, X. Numerical method for two dimensional fractional reaction subdiffusion equation. Eur. Phys. J. Spec. Top. 222, 1961–1973 (2013). https://doi.org/10.1140/epjst/e2013-01977-9

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  • DOI: https://doi.org/10.1140/epjst/e2013-01977-9

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