A finite difference method with non-uniform timesteps for fractional diffusion equations

Computer Physics Communications

Volumn 183, Issue 12, 2012, Pages 2594-2600

  Yuste, Santos B ^a   Quintana Murillo, Joaquín ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

Adaptive numerical methods; Anomalous diffusion; Finite difference methods; Fractional diffusion equations; Non uniform meshes

Indexed keywords

ADAPTIVE METHODS; ANOMALOUS DIFFUSION; COMPUTATIONAL ADVANTAGES; COMPUTATIONAL COSTS; FRACTIONAL DIFFUSION EQUATION; GENERAL CLASS; IMPLICIT FINITE DIFFERENCE METHOD; NON-UNIFORM MESH; NUMERICAL ERRORS; POINT SOURCES; STEP METHOD; UNCONDITIONALLY STABLE;

NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

FINITE DIFFERENCE METHOD;

EID: 84865615010     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2012.07.011     Document Type: Article

References (39)

1. K.B. Oldham, and J. Spanier The Fractional Calculus 1974 Academic Press New York
2. R. Hilfer, Applications of Fractional Calculus in Physics 2000 World Scientific Singapore
3. R. Metzler, and J. Klafter Phys. Rep. 339 2000 1
4. I.M. Sokolov, J. Klafter, and A. Blumen Phys. Today 55 2002 48
5. R. Metzler, and J. Klafter J. Phys. A: Math. Gen. 37 2004 R161
6. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier Amsterdam
7. R. Klages, G. Radons, I.M. Sokolov, Anomalous Transport: Foundations and Applications 2008 Elsevier Amsterdam
8. R.L. Magin, O. Abdullah, D. Baleanu, and X.J. Zhou J. Magn. Reson. 190 2008 255
9. J.A. Dix, and A.S. Verkman Annu. Rev. Biophys. 37 2008 247
10. B.I. Henry, T.A.M. Langlands, and S. Wearne Phys. Rev. Lett. 100 2008 128103
11. E. Barkai, R. Metzler, and J. Klafter Phys. Rev. E 61 2000 132
12. S.B. Yuste, and L. Acedo Physica A 336 2004 334
13. A.M.A. El-Sayed, and M. Gaber Phys. Lett. A 359 2006 175
14. H. Jafari, and S. Momani Phys. Lett. A 370 2007 388
15. S.S. Ray Phys. Scr. 75 2007 53
16. R. Gorenflo, F. Mainardi, D. Moretti, and P. Paradisi Nonlinear Dynam. 29 2002 129
17. S.B. Yuste, and L. Acedo SIAM J. Numer. Anal. 42 2005 1862
18. S.B. Yuste J. Comput. Phys. 216 1 2006 264
19. V.E. Lynch, B.A. Carreras, D. del-Castillo-Negrete, K.M. Ferreira-Mejias, and H.R. Hicks J. Comput. Phys. 192 2003 406
20. M.M. Meerschaert, and C. Tadjeran J. Comput. Appl. Math. 172 2004 65
21. C.M. Chen, F. Liu, I. Turner, and V. Anh J. Comput. Phys. 227 2007 886
22. Z.Z. Sun, and X. Wu Appl. Numer. Math. 56 2006 193
23. I. Podlubny, A.V. Chechkin, T. Skovranek, Y. Chen, and B.M. Vinagre J. Comput. Phys. 228 2009 3137
24. M. Cui J. Comput. Phys. 228 2009 7792
25. H. Brunner, L. Ling, and M. Yamamoto J. Comput. Phys. 229 2010 6613
26. T. Skovranek, V.V. Verbickij, Y. Tarte, I. Podlubny, Discretization of fractional-order operators and fractional differential equations on a non-equidistant mesh, Article no. FDA10-062, in: I. Podlubny, B.M. Vinagre Jara, Y.Q. Chen, V. Feliu Batlle, I. Tejado Balsera (Eds.), Proceedings of FDA10, the 4th IFAC Workshop Fractional Differentiation and its Applications, Badajoz, 2010, p. 18.
27. K. Mustapha, and W. McLean Numer. Algorithms 56 2011 159
28. K. Diethelm, N.J. Ford, and A.D. Freed Nonlinear Dynam. 29 2002 3
29. K. Diethelm, N.J. Ford, A.D. Freed, and Yu. Luchko Comput. Methods Appl. Mech. Engrg. 194 2005 743
30. N.J. Ford, and A.C. Simpson Numer. Algorithms 26 2001 333
31. D.A. Murio Comput. Math. Appl. 56 2008 1138
32. S.B. Yuste, and J. Quintana-Murillo Phys. Scr. T136 2009 014025
33. F. Liu, P. Zhuang, V. Anh, and I. Turner ANZIAM J. 47 2006 C48
34. R.J. LeVeque Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems 2007 SIAM Philadelfia
35. J. Quintana-Murillo, and S.B. Yuste J. Comput. Nonlinear Dyn. 6 2011 021014
36. K.W. Morton, and D.F. Mayers Numerical Solution of Partial Differential Equations 1994 Cambridge University Press Cambridge
37. G. Allaire Numerical Analysis and Optimization: An Introduction to Mathematical Modelling and Numerical Simulation 2007 Oxford University Press New York
38. A.M. Mathai, and R.K. Saxena The H-Function with Applications in Statistics and Other Disciplines 1978 Wiley New York
39. S.B. Yuste, E. Abad, and K. Lindenberg Phys. Rev. E 82 2010 061123