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Volumn 22, Issue 3, 2006, Pages 87-99

Implicit difference approximation for the time fractional diffusion equation

Author keywords

convergence; Fractional differential equation; implicit difference approximation; stability

Indexed keywords


EID: 84867978055     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02832039     Document Type: Article
Times cited : (238)

References (19)
  • 1
    • 0036650559 scopus 로고    scopus 로고
    • Solution for a Fractional Diffusion-Wave Equation Defined in a Bounded Domain
    • 1009.65085 10.1023/A:1016539022492
    • O. P. Agrawal 2002 Solution for a Fractional Diffusion-Wave Equation Defined in a Bounded Domain J. Nonlinear Dynamics 29 145 155 1009.65085 10.1023/A:1016539022492
    • (2002) J. Nonlinear Dynamics , vol.29 , pp. 145-155
    • Agrawal, O.P.1
  • 2
    • 0035538580 scopus 로고    scopus 로고
    • Spectral analysis of fractional kinetic equations with random data
    • 1034.82044 10.1023/A:1010474332598 1859007
    • V. V. Anh N. N. Leonenko 2001 Spectral analysis of fractional kinetic equations with random data J. Stat. Pgys. 104 1349 1387 1034.82044 10.1023/A:1010474332598 1859007
    • (2001) J. Stat. Pgys. , vol.104 , pp. 1349-1387
    • Anh, V.V.1    Leonenko, N.N.2
  • 3
    • 0742323831 scopus 로고    scopus 로고
    • Time-fractional telegraph equations and telegraph processes with Brownian time
    • 1049.60062 10.1007/s00440-003-0309-8 2027298
    • Orsingher Enzo Beghin Luisa 2004 Time-fractional telegraph equations and telegraph processes with Brownian time Probab. Theory Related Fields 128 1 141 160 1049.60062 10.1007/s00440-003-0309-8 2027298
    • (2004) Probab. Theory Related Fields , vol.128 , Issue.1 , pp. 141-160
    • Orsingher1    Enzo2    Beghin3    Luisa4
  • 4
    • 14644446063 scopus 로고    scopus 로고
    • Least squares finite element solution of a fractional order two-point boundary value problem
    • 1069.65094 10.1016/j.camwa.2004.10.003 2107380
    • G. J. Fix J. P. Roop 2004 Least squares finite element solution of a fractional order two-point boundary value problem Computers Math. Applic. 48 1017 1033 1069.65094 10.1016/j.camwa.2004.10.003 2107380
    • (2004) Computers Math. Applic. , vol.48 , pp. 1017-1033
    • Fix, G.J.1    Roop, J.P.2
  • 5
    • 0001859930 scopus 로고    scopus 로고
    • Maping between solusions of fractional diffusion-wave equations
    • 1033.35161 1743407
    • R. Gorenflo A. Iskenderov Yu. Luchko 2000 Maping between solusions of fractional diffusion-wave equations Fract. Calculus and Appl. Math. 3 75 86 1033.35161 1743407
    • (2000) Fract. Calculus and Appl. Math. , vol.3 , pp. 75-86
    • Gorenflo, R.1    Iskenderov, A.2    Luchko, Yu.3
  • 6
    • 0000103589 scopus 로고    scopus 로고
    • Wright function as scale-invariant solutions of the diffusion-wave equation
    • 0973.35012 10.1016/S0377-0427(00)00288-0 1765948
    • R. Gorenflo Yu. Luchko F. Mainardi 2000 Wright function as scale-invariant solutions of the diffusion-wave equation J. Comp. Appl. Math. 118 175 191 0973.35012 10.1016/S0377-0427(00)00288-0 1765948
    • (2000) J. Comp. Appl. Math. , vol.118 , pp. 175-191
    • Gorenflo, R.1    Luchko, Yu.2    Mainardi, F.3
  • 7
    • 0036650850 scopus 로고    scopus 로고
    • Time Fractional Diffusion: A Discrete Random Walk Approach [J]
    • 1009.82016 10.1023/A:1016547232119 1926470
    • R. Gorenflo F. Mainardi D. Moretti P. Paradisi 2002 Time Fractional Diffusion: A Discrete Random Walk Approach [J] Nonlinear Dynamics 29 129 143 1009.82016 10.1023/A:1016547232119 1926470
    • (2002) Nonlinear Dynamics , vol.29 , pp. 129-143
    • Gorenflo, R.1    Mainardi, F.2    Moretti, D.3    Paradisi, P.4
  • 8
    • 33747286487 scopus 로고    scopus 로고
    • The time fractional diffusion and advection-dispersion equation
    • 2124926 10.1017/S1446181100008282
    • F. Huang F. Liu 2005 The time fractional diffusion and advection-dispersion equation ANZIAM J. 46 1 14 2124926 10.1017/ S1446181100008282
    • (2005) ANZIAM J. , vol.46 , pp. 1-14
    • Huang, F.1    Liu, F.2
  • 9
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of space fractional Fokker-Planck equation
    • 1036.82019 10.1016/j.cam.2003.09.028 2057973
    • Liu V. Anh I. Turner 2004 Numerical solution of space fractional Fokker-Planck equation J. Comp. and Appl. Math. 166 209 219 1036.82019 10.1016/j.cam.2003.09.028 2057973
    • (2004) J. Comp. and Appl. Math. , vol.166 , pp. 209-219
    • Liu1    Anh, V.2    Turner, I.3
  • 10
    • 0348230399 scopus 로고    scopus 로고
    • Time fractional advection dispersion equation
    • 1068.26006 2000212
    • F. Liu V. Anh I. Turner P. Zhuang 2003 Time fractional advection dispersion equation J. Appl. Math. & Computing 13 233 245 1068.26006 2000212
    • (2003) J. Appl. Math. & Computing , vol.13 , pp. 233-245
    • Liu, F.1    Anh, V.2    Turner, I.3    Zhuang, P.4
  • 11
    • 33751548431 scopus 로고    scopus 로고
    • Numerical simulation for solute transport in fractal porous media
    • 2180945
    • F. Liu V. Anh I. Turner P. Zhuang 2004 Numerical simulation for solute transport in fractal porous media ANZIAM J. 45 E 461 473 2180945
    • (2004) ANZIAM J. , vol.45 , Issue.E , pp. 461-473
    • Liu, F.1    Anh, V.2    Turner, I.3    Zhuang, P.4
  • 12
    • 33751533397 scopus 로고    scopus 로고
    • Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation
    • 2182183
    • F. Liu S. Shen V. Anh I. Turner 2005 Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation ANZIAM J. 46 E 488 504 2182183
    • (2005) ANZIAM J. , vol.46 , Issue.E , pp. 488-504
    • Liu, F.1    Shen, S.2    Anh, V.3    Turner, I.4
  • 13
    • 34848861554 scopus 로고    scopus 로고
    • The telegraph processes stopped at stable-distributed times and its connection with the fractional telegraph equation
    • 1083.60039 2035414
    • B. Luisa O. Enzo 2003 The telegraph processes stopped at stable-distributed times and its connection with the fractional telegraph equation Fract. Calc. Appl. Anal. 6 2 187 204 1083.60039 2035414
    • (2003) Fract. Calc. Appl. Anal. , vol.6 , Issue.2 , pp. 187-204
    • Luisa, B.1    Enzo, O.2
  • 14
    • 30244460855 scopus 로고    scopus 로고
    • The fundamental solutions for the fractional diffusiona-wave equation
    • 0879.35036 1419811
    • F. Mainardi 1996 The fundamental solutions for the fractional diffusiona-wave equation Appl. Math. 9 6 23 28 0879.35036 1419811
    • (1996) Appl. Math. , vol.9 , Issue.6 , pp. 23-28
    • Mainardi, F.1
  • 16
    • 84867989343 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • in press
    • M. Meerschaert and C. Tadjeran,Finite difference approximations for fractional advection-dispersion flow equations, J. Comp. and Appl. Math. (2005), (in press).
    • (2005) J. Comp. and Appl. Math.
    • Meerschaert, M.1    Tadjeran, C.2
  • 18
    • 0001553919 scopus 로고
    • Fractional diffusion and wave equations
    • 0692.45004 10.1063/1.528578 974464
    • W. R. Schneider W. Wyss 1989 Fractional diffusion and wave equations J. Math. Phys. 30 134 144 0692.45004 10.1063/1.528578 974464
    • (1989) J. Math. Phys. , vol.30 , pp. 134-144
    • Schneider, W.R.1    Wyss, W.2
  • 19
    • 0009481303 scopus 로고
    • The fractional diffusion equation
    • 0632.35031 10.1063/1.527251 861345
    • W. Wyss 1986 The fractional diffusion equation J. Math. Phys. 27 2782 2785 0632.35031 10.1063/1.527251 861345
    • (1986) J. Math. Phys. , vol.27 , pp. 2782-2785
    • Wyss, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.