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Volumn 216, Issue 1, 2006, Pages 264-274

Weighted average finite difference methods for fractional diffusion equations

Author keywords

Anomalous diffusion; Finite difference methods; Fractional diffusion equation; von Neumann stability analysis

Indexed keywords

DIFFUSION; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; STABILITY CRITERIA; STATISTICAL METHODS;

EID: 33646128485     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.12.006     Document Type: Article
Times cited : (341)

References (36)
  • 3
    • 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. Rep. 339 (2000) 1-77
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 4
    • 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: Math. Gen. 37 (2004) R161-R208
    • (2004) J. Phys. A: Math. Gen. , vol.37
    • Metzler, R.1    Klafter, J.2
  • 5
    • 18144408075 scopus 로고    scopus 로고
    • Anomalous diffusion and relaxation close to thermal equilibrium: a fractional Fokker-Planck equation approach
    • Metzler R., Barkai E., and Klafter J. Anomalous diffusion and relaxation close to thermal equilibrium: a fractional Fokker-Planck equation approach. Phys. Rev. Lett. 82 (1999) 3563-3567
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 3563-3567
    • Metzler, R.1    Barkai, E.2    Klafter, J.3
  • 6
    • 0000078998 scopus 로고    scopus 로고
    • From continuous time random walks to the fractional Fokker-Planck equation
    • Barkai E., Metzler R., and Klafter J. From continuous time random walks to the fractional Fokker-Planck equation. Phys. Rev. E 61 (2000) 132-138
    • (2000) Phys. Rev. E , vol.61 , pp. 132-138
    • Barkai, E.1    Metzler, R.2    Klafter, J.3
  • 7
    • 41349096645 scopus 로고    scopus 로고
    • Fractional diffusion modeling of ion gating
    • Goychuk I., and Hänggi P. Fractional diffusion modeling of ion gating. Phys. Rev. E 70 (2004) 051915-1-051915-9
    • (2004) Phys. Rev. E , vol.70
    • Goychuk, I.1    Hänggi, P.2
  • 8
    • 85190293368 scopus 로고    scopus 로고
    • A. Iomin, S. Dorfman, L. Dorfman, On tumor development: fractional transport approach, preprint: .
  • 9
    • 20444465327 scopus 로고    scopus 로고
    • Fractional dynamics of interfaces between soft-nanoparticles and rough substrates
    • Chow T.S. Fractional dynamics of interfaces between soft-nanoparticles and rough substrates. Phys. Lett. A 342 (2005) 148-155
    • (2005) Phys. Lett. A , vol.342 , pp. 148-155
    • Chow, T.S.1
  • 10
    • 0000993220 scopus 로고
    • Anomalous diffusion in one dimension
    • Balakrishnan V. Anomalous diffusion in one dimension. Physica A 132 (1985) 569-580
    • (1985) Physica A , vol.132 , pp. 569-580
    • Balakrishnan, V.1
  • 11
    • 0009481303 scopus 로고
    • Fractional diffusion equation
    • Wyss W. Fractional diffusion equation. J. Math. Phys. 27 (1986) 2782-2785
    • (1986) J. Math. Phys. , vol.27 , pp. 2782-2785
    • Wyss, W.1
  • 12
    • 0001553919 scopus 로고
    • Fractional diffusion and wave equations
    • Schneider W.R., and Wyss W. Fractional diffusion and wave equations. J. Math. Phys. 30 (1989) 134-144
    • (1989) J. Math. Phys. , vol.30 , pp. 134-144
    • Schneider, W.R.1    Wyss, W.2
  • 13
    • 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
  • 14
    • 0001754759 scopus 로고
    • A numerical method for a partial integro-differential equation
    • Sanz-Serna J.M. A numerical method for a partial integro-differential equation. SIAM J. Numer. Anal. 25 (1988) 319-327
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 319-327
    • Sanz-Serna, J.M.1
  • 15
    • 0025383598 scopus 로고
    • A difference scheme for a nonlinear partial integrodifferential equation
    • López-Marcos J. A difference scheme for a nonlinear partial integrodifferential equation. SIAM J. Numer. Anal. 27 (1990) 20-31
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 20-31
    • López-Marcos, J.1
  • 16
    • 0001797959 scopus 로고
    • Numerical solution of an evolution equation with a positive-type memory term
    • McLean W., and Thomée V. Numerical solution of an evolution equation with a positive-type memory term. J. Aust. Math. Soc. Ser. B 35 (1993) 23-70
    • (1993) J. Aust. Math. Soc. Ser. B , vol.35 , pp. 23-70
    • McLean, W.1    Thomée, V.2
  • 17
    • 0030123212 scopus 로고    scopus 로고
    • Discretization with variable time steps of an evolution equation with a positive-type memory term
    • McLean W., Thomée V., and Wahlbin L.B. Discretization with variable time steps of an evolution equation with a positive-type memory term. J. Comp. Appl. Math. 69 (1996) 49-69
    • (1996) J. Comp. Appl. Math. , vol.69 , pp. 49-69
    • McLean, W.1    Thomée, V.2    Wahlbin, L.B.3
  • 18
    • 38249000368 scopus 로고
    • On the discretization in time for a parabolic integrodifferential equation with a weakly singular kernel I: smooth initial data
    • Da X. On the discretization in time for a parabolic integrodifferential equation with a weakly singular kernel I: smooth initial data. Appl. Math. Comput. 58 (1993) 1-27
    • (1993) Appl. Math. Comput. , vol.58 , pp. 1-27
    • Da, X.1
  • 19
    • 0030364596 scopus 로고    scopus 로고
    • Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
    • Lubich CH., Sloan I.H., and Thomée V. Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term. Math. Comp. 65 (1996) 1-17
    • (1996) Math. Comp. , vol.65 , pp. 1-17
    • Lubich, CH.1    Sloan, I.H.2    Thomée, V.3
  • 21
    • 85190251396 scopus 로고    scopus 로고
    • M. Ciesielski, J. Leszczynski, Numerical simulations of anomalous diffusion, 2003, preprint: .
  • 23
    • 85190264555 scopus 로고    scopus 로고
    • S.B. Yuste, Weighted average finite difference methods for fractional diffusion equations, in: A. Le Méhauté, J.A. Tenreiro Machado, J.C. Trigeassou, J. Sabatier (Eds.), Proceedings of the 1st IFAC Workshop on Fractional Differentiation and its Applications, ENSEIRB, Bordeaux, 2004, pp. 335-340.
  • 24
    • 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
    • 17144427014 scopus 로고    scopus 로고
    • The accuracy and stability of an implicit solution method for the fractional diffusion equation
    • Langlands T.A.M., and Henry B.I. The accuracy and stability of an implicit solution method for the fractional diffusion equation. J. Comput. Phys. 205 (2005) 719-736
    • (2005) J. Comput. Phys. , vol.205 , pp. 719-736
    • Langlands, T.A.M.1    Henry, B.I.2
  • 27
    • 25444472344 scopus 로고    scopus 로고
    • An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations
    • Yuste S.B., and Acedo L. An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations. SIAM J. Numer. Anal. 42 (2005) 1862-1874
    • (2005) SIAM J. Numer. Anal. , vol.42 , pp. 1862-1874
    • Yuste, S.B.1    Acedo, L.2
  • 28
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • Lubich Ch. Discretized fractional calculus. SIAM J. Math. Anal. 17 (1986) 704-719
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 704-719
    • Lubich, Ch.1
  • 32
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: some numerical methods
    • Carpinteri A., and Mainardi F. (Eds), Springer-Verlag, New York
    • Gorenflo R. Fractional calculus: some numerical methods. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer-Verlag, New York 277-290
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 277-290
    • Gorenflo, R.1
  • 33
    • 85190253110 scopus 로고    scopus 로고
    • K. Diethelm, J.M. Ford, N.J. Ford, M. Weilbeer, A comparison of backward differentiation approaches for ordinary and partial differential equations of fractional order, in: A. Le Méhauté, J.A. Tenreiro Machado, J.C. Trigeassou, J. Sabatier (Eds.), Proceedings of the 1st IFAC Workshop on Fractional Differentiation and its Applications, ENSEIRB, Bordeaux, 2004, pp. 353-358.
  • 34
    • 31144434675 scopus 로고    scopus 로고
    • From diffusion to anomalous diffusion: a century after Einstein's Brownian motion
    • Sokolov I.M., and Klafter J. From diffusion to anomalous diffusion: a century after Einstein's Brownian motion. Chaos 15 (2005) 026103-026109
    • (2005) Chaos , vol.15 , pp. 026103-026109
    • Sokolov, I.M.1    Klafter, J.2
  • 35
    • 0034257243 scopus 로고    scopus 로고
    • Accelerating Brownian motion: a fractional dynamics approach to fast diffusion
    • Metzler R., and Klafter J. Accelerating Brownian motion: a fractional dynamics approach to fast diffusion. Europhys. Lett. 51 (2000) 492-498
    • (2000) Europhys. Lett. , vol.51 , pp. 492-498
    • Metzler, R.1    Klafter, J.2
  • 36
    • 0036650559 scopus 로고    scopus 로고
    • Solution for a fractional diffusion-wave equation defined in a bounded domain
    • Agrawal O.P. Solution for a fractional diffusion-wave equation defined in a bounded domain. Nonlin. Dynam. 29 (2002) 145-155
    • (2002) Nonlin. Dynam. , vol.29 , pp. 145-155
    • Agrawal, O.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.