메뉴 건너뛰기




Volumn 61, Issue 8, 2011, Pages 946-960

A characteristic difference method for the transient fractional convection-diffusion equations

Author keywords

Finite difference methods; Fractional convection diffusion equations; Method of characteristics; Shifted Gr nwald Letnikov formula; Stability analysis

Indexed keywords

CHARACTERISTIC DIFFERENCE; CHARACTERISTIC METHOD; CONVECTION-DIFFUSION EQUATIONS; ERROR ESTIMATES; FRACTIONAL CONVECTION-DIFFUSION EQUATIONS; METHOD OF CHARACTERISTICS; NUMERICAL EXPERIMENTS; STABILITY ANALYSIS;

EID: 79956206224     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2011.02.007     Document Type: Article
Times cited : (28)

References (31)
  • 1
    • 0035014974 scopus 로고    scopus 로고
    • Subordinated advection-dispersion equation for contaminant transport
    • DOI 10.1029/2000WR900409
    • B. Baeumer, M.M. Meerschaert, D.A. Benson, and S.W. Wheatcraft Subordinated advection-dispersion equation for contaminant transport Water Resour. Res. 37 2001 1543 1550 (Pubitemid 32480655)
    • (2001) Water Resources Research , vol.37 , Issue.6 , pp. 1543-1550
    • Baeumer, B.1    Benson, D.A.2    Meerschaert, M.M.3    Wheatcraft, S.W.4
  • 2
    • 0034113992 scopus 로고    scopus 로고
    • The fractional-order governing equation of Levy motion
    • DOI 10.1029/2000WR900032
    • D. Benson, S.W. Wheatcraft, and M.M. Meerschaert The fractional-order governing equation of Lévy motion Water Resour. Res. 36 2000 1413 1423 (Pubitemid 30334242)
    • (2000) Water Resources Research , vol.36 , Issue.6 , pp. 1413-1423
    • Benson, D.A.1    Wheatcraft, S.W.2    Meerschaert, M.M.3
  • 3
    • 0034032484 scopus 로고    scopus 로고
    • Application of a fractional advection-dispersion equation
    • D. Benson, S.W. Wheatcraft, and M.M. Meerschaert Application of a fractional advection-dispersion equation Water Resour. Res. 36 2000 1403 1413
    • (2000) Water Resour. Res. , vol.36 , pp. 1403-1413
    • Benson, D.1    Wheatcraft, S.W.2    Meerschaert, M.M.3
  • 5
    • 51749116733 scopus 로고    scopus 로고
    • Finite difference approximations for the fractional Fokker-Planck equation
    • S. Chen, F. Liu, P. Zhuang, and V. Anh Finite difference approximations for the fractional Fokker-Planck equation Appl. Math. Modelling 33 2009 256 273
    • (2009) Appl. Math. Modelling , vol.33 , pp. 256-273
    • Chen, S.1    Liu, F.2    Zhuang, P.3    Anh, V.4
  • 7
    • 59349113701 scopus 로고    scopus 로고
    • Finite element method for the space and time fractional Fokker-Planck equation
    • W. Deng Finite element method for the space and time fractional Fokker-Planck equation SIAM J. Numer. Anal. 47 2008 204 226
    • (2008) SIAM J. Numer. Anal. , vol.47 , pp. 204-226
    • Deng, W.1
  • 8
    • 0001235787 scopus 로고
    • Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures
    • J. Douglas, and T.F. Russell Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures SIAM J. Numer. Anal. 19 1982 871 885
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 871-885
    • Douglas, J.1    Russell, T.F.2
  • 9
    • 42649109055 scopus 로고    scopus 로고
    • Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation
    • DOI 10.1137/050642757
    • V.J. Ervin, N. Heuer, and J.P. Roop Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation SIAM J. Numer. Anal. 45 2007 572 591 (Pubitemid 351599168)
    • (2007) SIAM Journal on Numerical Analysis , vol.45 , Issue.2 , pp. 572-591
    • Ervin, V.J.1    Heuer, N.2    Roop, J.P.3
  • 12
    • 34547548712 scopus 로고    scopus 로고
    • Finite difference/spectral approximations for the time-fractional diffusion equation
    • Y. Lin, and C. Xu Finite difference/spectral approximations for the time-fractional diffusion equation J. Comput. Phys. 225 2007 1533 1552
    • (2007) J. Comput. Phys. , vol.225 , pp. 1533-1552
    • Lin, Y.1    Xu, C.2
  • 13
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of the space fractional Fokker-Planck equation
    • DOI 10.1016/j.cam.2003.09.028, PII S0377042703008616
    • F. Liu, V. Anh, and I. Turner Numerical solution of the space fractional Fokker-Planck equation J. Comput. Appl. Math. 166 2004 209 219 (Pubitemid 38342127)
    • (2004) Journal of Computational and Applied Mathematics , vol.166 , Issue.1 , pp. 209-219
    • Liu, F.1    Anh, V.2    Turner, I.3
  • 14
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • C. Lubich Discretized fractional calculus SIAM J. Math. Anal. 17 1986 704 719
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 704-719
    • Lubich, C.1
  • 16
    • 28044468843 scopus 로고    scopus 로고
    • Finite difference approximations for two-sided space-fractional partial differential equations
    • DOI 10.1016/j.apnum.2005.02.008, PII S0168927405000590
    • M.M. Meerschaert, and C. Tadjeran Finite difference approximations for two-sided space-fractional partial differential equations Appl. Numer. Math. 56 2006 80 90 (Pubitemid 41690768)
    • (2006) Applied Numerical Mathematics , vol.56 , Issue.1 , pp. 80-90
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 17
    • 25444463578 scopus 로고    scopus 로고
    • Finite difference methods for two-dimensional fractional dispersion equation
    • DOI 10.1016/j.jcp.2005.05.017, PII S0021999105002731
    • M.M. Meerschaert, H.P. Scheffler, and C. Tadjeran Finite difference methods for two-dimensional fractional dispersion equation J. Comput. Phys. 211 2006 249 261 (Pubitemid 41363984)
    • (2006) Journal of Computational Physics , vol.211 , Issue.1 , pp. 249-261
    • Meerschaert, M.M.1    Scheffler, H.-P.2    Tadjeran, C.3
  • 20
    • 61349186917 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus II: Partial fractional differential equations
    • I. Podlubny, A. Chechkin, T. Skovranek, Y. Chen, and B.M. Vinagre Jara Matrix approach to discrete fractional calculus II: partial fractional differential equations J. Comput. Phys. 228 2009 3137 3153
    • (2009) J. Comput. Phys. , vol.228 , pp. 3137-3153
    • Podlubny, I.1    Chechkin, A.2    Skovranek, T.3    Chen, Y.4    Vinagre Jara, B.M.5
  • 21
    • 0036949980 scopus 로고    scopus 로고
    • Waiting-times and returns in high-frequency financial data: An empirical study
    • M. Raberto, E. Scalas, and F. Mainardi Waiting-times and returns in high-frequency financial data: an empirical study Phys. 314 2002 749 755
    • (2002) Phys. , vol.314 , pp. 749-755
    • Raberto, M.1    Scalas, E.2    Mainardi, F.3
  • 23
    • 64049113904 scopus 로고    scopus 로고
    • Finite difference approximates for a fractional advection diffusion problem
    • E. Sousa Finite difference approximates for a fractional advection diffusion problem J. Comput. Phys. 228 2009 4038 4054
    • (2009) J. Comput. Phys. , vol.228 , pp. 4038-4054
    • Sousa, E.1
  • 24
    • 74249113616 scopus 로고    scopus 로고
    • Finite difference approximations for the fractional advection-diffusion equation
    • L. Su, W. Wang, and Z. Yang Finite difference approximations for the fractional advection-diffusion equation Phys. Lett. A 373 2009 4405 4408
    • (2009) Phys. Lett. A , vol.373 , pp. 4405-4408
    • Su, L.1    Wang, W.2    Yang, Z.3
  • 25
    • 78649918171 scopus 로고    scopus 로고
    • Finite difference methods for fractional dispersion equations
    • L. Su, W. Wang, and Q. Xu Finite difference methods for fractional dispersion equations Appl. Math. Comput. 216 2010 3329 3334
    • (2010) Appl. Math. Comput. , vol.216 , pp. 3329-3334
    • Su, L.1    Wang, W.2    Xu, Q.3
  • 26
    • 33845628108 scopus 로고    scopus 로고
    • A second-order accurate numerical method for the two-dimensional fractional diffusion equation
    • DOI 10.1016/j.jcp.2006.05.030, PII S0021999106002610
    • C. Tadjeran, and M.M. Meerschaert A second-order accurate numerical method for the two-dimensional fractional diffusion equation J. Comput. Phys. 220 2007 813 823 (Pubitemid 44942995)
    • (2007) Journal of Computational Physics , vol.220 , Issue.2 , pp. 813-823
    • Tadjeran, C.1    Meerschaert, M.M.2
  • 27
    • 31744438550 scopus 로고    scopus 로고
    • A second-order accurate numerical approximation for the fractional diffusion equation
    • DOI 10.1016/j.jcp.2005.08.008, PII S0021999105003773
    • C. Tadjeran, M.M. Meerschaert, and H.P. Scheffler A second-order accurate numerical approximation for the fractional diffusion equation J. Comput. Phys. 213 2006 205 213 (Pubitemid 43174872)
    • (2006) Journal of Computational Physics , vol.213 , Issue.1 , pp. 205-213
    • Tadjeran, C.1    Meerschaert, M.M.2    Scheffler, H.-P.3
  • 28
    • 0002885705 scopus 로고
    • A lower bounded for the smallest singular value of a matrix
    • J.M. Varah A lower bounded for the smallest singular value of a matrix Lin. Alg. Appl. 11 1975 3 5
    • (1975) Lin. Alg. Appl. , vol.11 , pp. 3-5
    • Varah, J.M.1
  • 30
    • 69249214155 scopus 로고    scopus 로고
    • Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
    • Q. Yang, F. Liu, and I. Turner Numerical methods for fractional partial differential equations with Riesz space fractional derivatives Appl. Math. Modelling 34 1 2010 200 218
    • (2010) Appl. Math. Modelling , vol.34 , Issue.1 , pp. 200-218
    • Yang, Q.1    Liu, F.2    Turner, I.3
  • 31
    • 84907893973 scopus 로고    scopus 로고
    • Numerical methods for the variable-order fractional advection-diffusion with a nonlinear source term
    • P. Zhuang, F. Liu, V. Anh, and I. Turner Numerical methods for the variable-order fractional advection-diffusion with a nonlinear source term SIAM J. Numer. Anal. 47 3 2009 1760 1781
    • (2009) SIAM J. Numer. Anal. , vol.47 , Issue.3 , pp. 1760-1781
    • Zhuang, P.1    Liu, F.2    Anh, V.3    Turner, I.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.