메뉴 건너뛰기




Volumn 206, Issue 2, 2007, Pages 1098-1115

Numerical approximation of Lévy-Feller diffusion equation and its probability interpretation

Author keywords

L vy Feller diffusion; Markovian random walk; Numerical approximation; Riesz Feller potential; Stability and convergence; Stable probability distributions

Indexed keywords

NUMERICAL ANALYSIS; PROBABILITY; PROBLEM SOLVING; THEOREM PROVING;

EID: 34249805393     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.09.017     Document Type: Article
Times cited : (45)

References (37)
  • 1
    • 34249829934 scopus 로고    scopus 로고
    • W. Feller, On a generalization of Marcel Riesz' potentials and the semi-groups generated by them, Meddelanden Lunds Universitets Matematiska Seminarium (Comm. Sém. Mathém. Université de Lund), Tome suppl. dédié a M. Riesz, Lund (1952) 73-81.
  • 2
    • 34249817348 scopus 로고    scopus 로고
    • W. Feller, An Introduction to Probability Theory and its Applications, vol. 2, second ed., Wiley, New York, 1971.
  • 3
    • 44049116564 scopus 로고
    • Fractional diffusion equation for transport phenomena in random media
    • Giona M., and Roman H.E. Fractional diffusion equation for transport phenomena in random media. Physica A 185 (1992) 87-97
    • (1992) Physica A , vol.185 , pp. 87-97
    • Giona, M.1    Roman, H.E.2
  • 4
    • 0032647143 scopus 로고    scopus 로고
    • Discrete random walk models for symmetric Lévy-Feller diffusion process
    • Gorenflo R., De Fabritiis G., and Mainardi F. Discrete random walk models for symmetric Lévy-Feller diffusion process. Physica A 269 (1999) 79-89
    • (1999) Physica A , vol.269 , pp. 79-89
    • Gorenflo, R.1    De Fabritiis, G.2    Mainardi, F.3
  • 5
    • 0000361678 scopus 로고    scopus 로고
    • Random walk models for space-fractional diffusion processes
    • Gorenflo R., and Mainardi F. Random walk models for space-fractional diffusion processes. Fract. Cal. Appl. Anal. 1 (1998) 167-191
    • (1998) Fract. Cal. Appl. Anal. , vol.1 , pp. 167-191
    • Gorenflo, R.1    Mainardi, F.2
  • 6
    • 34249809186 scopus 로고    scopus 로고
    • R. Gorenflo, F. Mainardi, Feller fractional diffusion and Lévy stable motions, Conference on Levy Processes: Theory and Applications, January 1999, pp. 18-22.
  • 7
    • 0345725412 scopus 로고    scopus 로고
    • Approximation of Lévy-Feller diffusion by random walk
    • Gorenflo R., and Mainardi F. Approximation of Lévy-Feller diffusion by random walk. J. Anal. Appl. 18 (1999) 231-246
    • (1999) J. Anal. Appl. , vol.18 , pp. 231-246
    • Gorenflo, R.1    Mainardi, F.2
  • 9
    • 0141996364 scopus 로고    scopus 로고
    • Fully discrete random walks for space-time fractional diffusion equations
    • Gorenflo R., and Vivoli A. Fully discrete random walks for space-time fractional diffusion equations. Signal Process. 83 (2003) 2411-2420
    • (2003) Signal Process. , vol.83 , pp. 2411-2420
    • Gorenflo, R.1    Vivoli, A.2
  • 15
    • 33744918752 scopus 로고    scopus 로고
    • Fractional diffusion and reflective boundary condition
    • Krepysheva N., Pietro L.Di., and Néel M.C. Fractional diffusion and reflective boundary condition. Physica A 368 (2006) 355-361
    • (2006) Physica A , vol.368 , pp. 355-361
    • Krepysheva, N.1    Pietro, L.Di.2    Néel, M.C.3
  • 16
    • 33344471905 scopus 로고    scopus 로고
    • N. Krepysheva, L.Di. Pietro, M.C. Néel, Space fractional advection-diffusion and reflective boundary conditions, Phys. Rev. E 73 (2006) 021104//1-9.
  • 18
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of the space fractional Fokker-Planck equation
    • Liu F., Anh V., and Turner I. Numerical solution of the space fractional Fokker-Planck equation. J. Comput. Appl. Math. 166 (2004) 209-219
    • (2004) J. Comput. Appl. Math. , vol.166 , pp. 209-219
    • Liu, F.1    Anh, V.2    Turner, I.3
  • 19
    • 33751548431 scopus 로고    scopus 로고
    • Numerical simulation for solute transport in fractal porous media
    • Liu F., Anh V., Turner I., and Zhuang P. Numerical simulation for solute transport in fractal porous media. ANZIAM J. 45 E (2004) 461-473
    • (2004) ANZIAM J. , vol.45 , Issue.E , pp. 461-473
    • Liu, F.1    Anh, V.2    Turner, I.3    Zhuang, P.4
  • 20
    • 33751533397 scopus 로고    scopus 로고
    • Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation
    • Liu F., Shen S., Anh V., and Turner I. Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation. ANZIAM J. 46 E (2005) 488-504
    • (2005) ANZIAM J. , vol.46 , Issue.E , pp. 488-504
    • Liu, F.1    Shen, S.2    Anh, V.3    Turner, I.4
  • 21
    • 34249783708 scopus 로고    scopus 로고
    • F. Liu, P. Zhuang, V. Anh, I. Turner, K. Burrage, Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation, Appl. Math. Comput., 2006, in press.
  • 22
    • 34249812451 scopus 로고    scopus 로고
    • Q. Liu, F. Liu, I. Turner and V. Anh, Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method, J. Phys. Comput., 2006, in press.
  • 23
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Mainardi F., Luchko an Y., and Pagnini G. The fundamental solution of the space-time fractional diffusion equation. Frac. Cal. Appl. Anal. 4 2 (2001) 153-192
    • (2001) Frac. Cal. Appl. Anal. , vol.4 , Issue.2 , pp. 153-192
    • Mainardi, F.1    Luchko an, Y.2    Pagnini, G.3
  • 24
    • 25444463578 scopus 로고    scopus 로고
    • Finite difference methods for two-dimensional fractional dispersion equation
    • Meerschaert M.M., Scheffler H., and Tadjeran C. Finite difference methods for two-dimensional fractional dispersion equation. J. Comput. Phys. 211 (2006) 249-261
    • (2006) J. Comput. Phys. , vol.211 , pp. 249-261
    • Meerschaert, M.M.1    Scheffler, H.2    Tadjeran, C.3
  • 25
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • Meerschaert M.M., and Tadjeran C. Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 172 (2004) 65-77
    • (2004) J. Comput. Appl. Math. , vol.172 , pp. 65-77
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 26
    • 0033884660 scopus 로고    scopus 로고
    • Boundary value problems for fractional diffusion equations
    • Metzler R., and Klafter J. Boundary value problems for fractional diffusion equations. Physica A 278 (2000) 107-125
    • (2000) Physica A , vol.278 , pp. 107-125
    • Metzler, R.1    Klafter, J.2
  • 27
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: a fractional dynamics approach
    • Metzler R., and Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Report 339 (2000) 1-77
    • (2000) Phys. Report , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 28
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics
    • Metzler R., and Klafter J. The restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 37 (2004) R161-R208
    • (2004) J. Phys. A , vol.37
    • Metzler, R.1    Klafter, J.2
  • 29
    • 31244438428 scopus 로고    scopus 로고
    • A physical interpretation for the fractional derivative in the Lévy diffusion
    • Molz III F.J., Fjx III G.J., and Lu S. A physical interpretation for the fractional derivative in the Lévy diffusion. Appl. Math. Lett. 15 (2002) 907-911
    • (2002) Appl. Math. Lett. , vol.15 , pp. 907-911
    • Molz III, F.J.1    Fjx III, G.J.2    Lu, S.3
  • 33
    • 70549107817 scopus 로고    scopus 로고
    • Error analysis of an explicit finite difference approximation for the space fractional diffusion with insulated ends
    • Shen S., and Liu F. Error analysis of an explicit finite difference approximation for the space fractional diffusion with insulated ends. ANZIAM J. 46 E (2005) 871-887
    • (2005) ANZIAM J. , vol.46 , Issue.E , pp. 871-887
    • Shen, S.1    Liu, F.2
  • 35
    • 14844296496 scopus 로고    scopus 로고
    • A probabilistic interpretation of the fractional order differentiation
    • Teneiro Machado J.A. A probabilistic interpretation of the fractional order differentiation. Frac. Cal. Appl. Anal. 6 1 (2003) 73-80
    • (2003) Frac. Cal. Appl. Anal. , vol.6 , Issue.1 , pp. 73-80
    • Teneiro Machado, J.A.1
  • 37
    • 84867978055 scopus 로고    scopus 로고
    • Implicit difference approximation for the time fractional diffusion equation
    • Zhuang P., and Liu F. Implicit difference approximation for the time fractional diffusion equation. J. Appl. Math. Comput. 22 3 (2006) 87-99
    • (2006) J. Appl. Math. Comput. , vol.22 , Issue.3 , pp. 87-99
    • Zhuang, P.1    Liu, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.