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Volumn 79, Issue 3, 2014, Pages 431-444

A novel numerical approximation for the space fractional advection-dispersion equation

Author keywords

consistency; convergence; Crank Nicolson scheme; Riesz fractional advection dispersion equation; second order accurate scheme; stability; weighted finite difference approximation scheme

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DISPERSIONS; FINITE DIFFERENCE METHOD; NUMERICAL METHODS;

EID: 84901456625     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxs073     Document Type: Article
Times cited : (45)

References (19)
  • 1
    • 84855207635 scopus 로고    scopus 로고
    • Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
    • elik, C. & Duman, M. (2012) Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative. J. Comput. Phys., 231, 1743-1750
    • (2012) J. Comput. Phys , vol.231 , pp. 1743-1750
    • Elik, C.1    Duman, M.2
  • 2
    • 49249094092 scopus 로고    scopus 로고
    • ADI-Euler and extrapolation methods for the two-dimension fractional advection-dispersion equation
    • Chen, S. & Liu, F. (2008) ADI-Euler and extrapolation methods for the two-dimension fractional advection-dispersion equation. J. Appl. Math. Comput., 26, 295-311
    • (2008) J. Appl. Math. Comput , vol.26 , pp. 295-311
    • Chen, S.1    Liu, F.2
  • 3
    • 76449102580 scopus 로고    scopus 로고
    • Adomian s decomposition method for solving an intermediate fractional advection-dispersion equation
    • EI-Sayed, A. M. A., Behiry, S. H. & Raslan, W. E. (2010) Adomian s decomposition method for solving an intermediate fractional advection-dispersion equation. Comput. Math. Appl., 59, 1759-1765
    • (2010) Comput. Math. Appl , vol.59 , pp. 1759-1765
    • Ei-Sayed, A.M.A.1    Behiry, S.H.2    Raslan, W.E.3
  • 4
    • 0345725412 scopus 로고    scopus 로고
    • Approximation of Lvy-Feller diffusion by random walk
    • Gorenflo, R. & Mainardi, F. (1999) Approximation of Lvy-Feller diffusion by random walk. J. Anal. Appl. (ZAA), 18, 231-246.
    • (1999) J. Anal. Appl. (ZAA , vol.18 , pp. 231-246
    • Gorenflo, R.1    Mainardi, F.2
  • 6
    • 79952454978 scopus 로고    scopus 로고
    • Numerical approaches to fractional calculus and fractional ordinary differential equation
    • Li, C., Chen, A. & amp; Ye, J. (2011) Numerical approaches to fractional calculus and fractional ordinary differential equation. J. Comput. Phys., 230, 3352-3368
    • (2011) J. Comput. Phys , vol.230 , pp. 3352-3368
    • Li, C.1    Chen, A.2    Ye, J.3
  • 7
    • 84861220597 scopus 로고    scopus 로고
    • Finite difference methods for fractional differential equations
    • Li, C. & Zeng, F. (2012) Finite difference methods for fractional differential equations. Int. J. Bifur. Chaos, 22, 1230014
    • (2012) Int. J. Bifur. Chaos , vol.22 , pp. 1230014
    • Li, C.1    Zeng, F.2
  • 8
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of space fractional Fokker-Planck equation
    • Liu, F., Anh, V. & Turner, I. (2004) Numerical solution of space fractional Fokker-Planck equation. J. Comp. Appl. Math., 166, 209-219
    • (2004) J. Comp. Appl. Math , vol.166 , pp. 209-219
    • Liu, F.1    Anh, V.2    Turner, I.3
  • 9
    • 33846798041 scopus 로고    scopus 로고
    • Approximation of the Lvy-Feller advection-dispersion process by random walk and finite difference method
    • Liu, Q., Liu, F., Turner, I. & Anh, V. (2007) Approximation of the Lvy-Feller advection-dispersion process by random walk and finite difference method. J. Comput. Phys., 222, 57-70
    • (2007) J. Comput. Phys , vol.222 , pp. 57-70
    • Liu, Q.1    Liu, F.2    Turner, I.3    Anh, V.4
  • 10
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractioanl advection-dispersion flow equations
    • Meerschaert, M. M. & Tadjeran, C. (2004) Finite difference approximations for fractioanl advection-dispersion flow equations. J. Comp. Appl. Math., 172, 65-77
    • (2004) J. Comp. Appl. Math , vol.172 , pp. 65-77
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 11
    • 0002641421 scopus 로고    scopus 로고
    • The random walks guide to anomalous diffusion: A fractional dynamics approach
    • Metzler, R. & Klafter, J. (2000) T he random walks guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep., 339, 1-77
    • (2000) Phys. Rep , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 12
    • 33744801528 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus
    • Podlubny, I. (2000) Matrix approach to discrete fractional calculus. Fract. Calc. Appl. Anal., 3, 359-386
    • (2000) Fract. Calc. Appl. Anal , vol.3 , pp. 359-386
    • Podlubny, I.1
  • 13
    • 61349186917 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus II: Partial fractional differential equations
    • Podlubny, I., Chechkin, A., Skovranek, T., Chen, Y. Q. & Blas M. Vinagre Jara (2009) Matrix approach to discrete fractional calculus II: Partial fractional differential equations. J. Comput. Phys ., 228, 3137-3153
    • (2009) J. Comput. Phys , vol.228 , pp. 3137-3153
    • Podlubny, I.1    Chechkin, A.2    Skovranek, T.3    Chen, Y.Q.4    Blas, M.5    Jara, V.6
  • 14
    • 33646191893 scopus 로고    scopus 로고
    • Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in R2
    • Roop, J. P. (2006) Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in R2. J. Comput. Appl. Math., 193, 243-268
    • (2006) J. Comput. Appl. Math , vol.193 , pp. 243-268
    • Roop, J.P.1
  • 16
    • 79951851714 scopus 로고    scopus 로고
    • Numerical approxima tions and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation
    • Shen, S., Liu, F. & Anh, V. (2011) Numerical approxima tions and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation. Numer. Algorithms, 56, 383-403
    • (2011) Numer. Algorithms , vol.56 , pp. 383-403
    • Shen, S.1    Liu, F.2    Anh, V.3
  • 17
    • 57649137996 scopus 로고    scopus 로고
    • The fundamental solut ion and numerical solution of the Riesz fractional advection-dispersion eqution
    • Shen, S., Liu, F., Anh, V. & Turner, I. (2008) The fundamental solut ion and numerical solution of the Riesz fractional advection-dispersion eqution. IMA J. Appl. Math., 73, 850-872
    • (2008) IMA J. Appl. Math , vol.73 , pp. 850-872
    • Shen, S.1    Liu, F.2    Anh, V.3    Turner, I.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.