Meshless computation for partial differential equations of fractional order

WIT Transactions on Modelling and Simulation

Volumn 52, Issue , 2011, Pages 333-343

  Wen, P H ^a   Hon, Y C ^b  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Durbin algorithm; Fractional derivatives; Laplace transform; Partial differential equations; Radial basis function

Indexed keywords

ADVECTION-DISPERSION EQUATION; FRACTIONAL DERIVATIVES; GROUND-WATER HYDROLOGY; INVERSION METHODS; NUMERICAL PROPERTIES; RADIAL BASIS FUNCTION INTERPOLATION; RADIAL BASIS FUNCTIONS; TRANSFORMED DOMAIN;

BOUNDARY ELEMENT METHOD; GROUNDWATER; LAPLACE TRANSFORMS; POROUS MATERIALS; RADIAL BASIS FUNCTION NETWORKS; TIME DOMAIN ANALYSIS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 84860463958     PISSN: 1743355X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2495/BE110291     Document Type: Conference Paper

References (22)

1. Ciesielski M. and Leszczynsky J., Numerical treatment of an initialboundary value problem for fractional partial differential equations, Signal Process 86 (2006), 2619-2631.
2. Barkai E., Metzler R., Klafter J., From continuous time random walks to the fractional Fokker-Planck equation, Phys. Rev. E 61 (2000) 132-138.
3. Blumen A., Zumofen G., Klafter J., Transport aspects in anomalous diffusion: Levy walks, Phys. Rev. A 40 (1989) 3964-3973.
4. Bouchaud J. P., Georges A., Anomalous diffusion in disordered media- statistical mechanisms, models and physical applications, Phys. Rep. 195 (1990) 127-293.
5. Chaves A., Fractional diffusion equation to describe Levy lights, Phys. Lett. A 239 (1998) 13-16.
6. Meerschaert M. M., Benson D., ScheXer H. P., Baeumer B., Stochastic solution of space-time fractional diffusion equations, Phys. Rev. E 65 (2002) 1103-1106.
7. Meerschaert M.M., ScheXer H. P., Semistable Levy Motion, Frac. Calc. Appl. Anal. 5 (2002) 27-54.
8. Zaslavsky G., Fractional kinetic equation for Hamiltonian chaos. Chaotic advection, tracer dynamics and turbulent dispersion, Phys. D 76 (1994) 110-122.
9. Raberto M., Scalas E., Mainardi F., Waiting-times and returns in highfrequency financial data: an empirical study, Physica A 314 (2002) 749-755.
10. Sabatelli L., Keating S., Dudley J., Richmond P., Waiting time distributions in financial markets, Eur. Phys. J. B 27 (2002) 273-275.
11. Baeumer B., Meerschaert M. M., Benson D., Wheatcraft S. W., Subordinated advection-dispersion equation for contaminant transport, Water Resour. Res. 37 (2001) 1543-1550.
12. Benson D., Wheatcraft S., Meerschaert M. M., Application of a fractional advection-dispersion equation, Water Resour. Res. 36 (2000) 1403-1412.
13. Chaves A., Fractional diffusion equation to describe Levy lights, Phys. Lett. A 239 (1998) 13-16.
14. Barkai E., Metzler R., Klafter J., From continuous time random walks to the fractional Fokker-Planck equation, Phys. Rev. E 61 (2000) 132-138.
15. Hardy R. L., Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res. 176, (1971) 1905-1915.
16. Franke, R., Scattered data interpolation: test of some methods, Math. Comput. 38, (1982) 181-200.
17. Kansa, E. J., Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics-I, Computers Math. Appl. 19(8/9), (1990) 127-145.
18. Madych, W. R., and Nelson, S. A., Multivariate interpolation and conditionally positive definite functions I, J. Approx. Theory and Its Appl. 4, (1988) 77-89.
19. Lynch V. E., Carreras B. A., del-Castillo-Negrete D., Ferreira-Mejias K. M., Hicks H. R., Numerical methods for the solution of partial differential equations of fractional order, Journal of Computational Physics 192 (2003) 406-421.
20. Durbin F., Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate's method. The Computer Journal 1975; 17:371-376.
21. Wen P. H., Chen C. S., The method of particular solutions for solving scalar wave equations. Commun. Numer. Meth. Engng. (2009).
22. Wen P. H., Aliabadi M. H., Rooke D. P., The influence of elastic waves on dynamic stress intensity factors (three dimensional problem). Archive of Applied Mechanics 1996; 66(6):384-385