메뉴 건너뛰기




Volumn 231, Issue 6, 2012, Pages 2621-2633

Compact alternating direction implicit method for two-dimensional time fractional diffusion equation

Author keywords

Alternating direction iterative method; Compact scheme; Finite difference; Fourier analysis; Fractional diffusion equation; Stability

Indexed keywords

DIFFUSION; FINITE DIFFERENCE METHOD; FOURIER ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 84856219458     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.12.010     Document Type: Article
Times cited : (126)

References (36)
  • 1
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: a fractional dynamics approach
    • Metzler R., Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 2000, 339:1-77.
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 4
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • Meerschaert M., Tadjeran C. Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 2004, 172:65-77.
    • (2004) J. Comput. Appl. Math. , vol.172 , pp. 65-77
    • Meerschaert, M.1    Tadjeran, C.2
  • 5
    • 17144427014 scopus 로고    scopus 로고
    • The accuracy and stability of an implicit solution method for the fractional diffusion equation
    • Langlands T.A.M., Henry B.I. The accuracy and stability of an implicit solution method for the fractional diffusion equation. J. Comput. Phys. 2005, 205:719-736.
    • (2005) J. Comput. Phys. , vol.205 , pp. 719-736
    • Langlands, T.A.M.1    Henry, B.I.2
  • 6
    • 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., Acedo L. An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations. SIAM J. Numer. Anal. 2005, 42(5):1862-1874.
    • (2005) SIAM J. Numer. Anal. , vol.42 , Issue.5 , pp. 1862-1874
    • Yuste, S.B.1    Acedo, L.2
  • 7
    • 33646128485 scopus 로고    scopus 로고
    • Weighted average finite difference methods for fractional diffusion equations
    • Yuste S.B. Weighted average finite difference methods for fractional diffusion equations. J. Comput. Phys. 2006, 216:264-274.
    • (2006) J. Comput. Phys. , vol.216 , pp. 264-274
    • Yuste, S.B.1
  • 8
    • 55549107511 scopus 로고    scopus 로고
    • New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation
    • Zhuang P., Liu F., Anh V., Turner I. New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation. SIAM J. Numer. Anal. 2008, 46(2):1079-1095.
    • (2008) SIAM J. Numer. Anal. , vol.46 , Issue.2 , pp. 1079-1095
    • Zhuang, P.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 9
    • 40849115179 scopus 로고    scopus 로고
    • Finite difference methods and a fourier analysis for the fractional reaction-subdiffusion equation
    • Chen C.-M., Liu F., Burrage K. Finite difference methods and a fourier analysis for the fractional reaction-subdiffusion equation. Appl. Math. Comput. 2008, 198:754-769.
    • (2008) Appl. Math. Comput. , vol.198 , pp. 754-769
    • Chen, C.-M.1    Liu, F.2    Burrage, K.3
  • 10
    • 61349186917 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus II: partial fractional differential equations
    • Podlubny I., Chechkin A., Skovranek T., Chen Y., Vinagre Jara B.M. Matrix approach to discrete fractional calculus II: partial fractional differential equations. J. Comput. Phys. 2009, 228:3137-3153.
    • (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
  • 11
    • 67349231192 scopus 로고    scopus 로고
    • Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term
    • Liu F., Yang C., Burrage K. Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term. J. Comput. Appl. Math. 2009, 231:160-176.
    • (2009) J. Comput. Appl. Math. , vol.231 , pp. 160-176
    • Liu, F.1    Yang, C.2    Burrage, K.3
  • 12
    • 77952888765 scopus 로고    scopus 로고
    • A compact difference scheme for the fractional diffusion-wave equation
    • Du R., Cao W.R., Sun Z.Z. A compact difference scheme for the fractional diffusion-wave equation. Appl. Math. Model. 2010, 34:2998-3007.
    • (2010) Appl. Math. Model. , vol.34 , pp. 2998-3007
    • Du, R.1    Cao, W.R.2    Sun, Z.Z.3
  • 13
    • 0003102291 scopus 로고
    • Higher order accurate difference solutions of fluid mechanics problems by a compact difference technique
    • Hirsch R.S. Higher order accurate difference solutions of fluid mechanics problems by a compact difference technique. J. Comput. Phys. 1975, 24:90-109.
    • (1975) J. Comput. Phys. , vol.24 , pp. 90-109
    • Hirsch, R.S.1
  • 14
    • 9144220381 scopus 로고
    • Compact finite difference schemes with spectral-like resolution
    • Lele S.K. Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 1992, 103:16-42.
    • (1992) J. Comput. Phys. , vol.103 , pp. 16-42
    • Lele, S.K.1
  • 15
    • 69049086472 scopus 로고    scopus 로고
    • Compact finite difference method for the fractional diffusion equation
    • Cui M.R. Compact finite difference method for the fractional diffusion equation. J. Comput. Phys. 2009, 228:7792-7804.
    • (2009) J. Comput. Phys. , vol.228 , pp. 7792-7804
    • Cui, M.R.1
  • 16
    • 78649334165 scopus 로고    scopus 로고
    • A compact finite difference scheme for the fractional sub-diffusion equations
    • Gao G.-H., Sun Z.-Z. A compact finite difference scheme for the fractional sub-diffusion equations. J. Comput. Phys. 2011, 230:586-595.
    • (2011) J. Comput. Phys. , vol.230 , pp. 586-595
    • Gao, G.-H.1    Sun, Z.-Z.2
  • 17
    • 25444463578 scopus 로고    scopus 로고
    • Finite difference methods for two-dimensional fractional dispersion equation
    • Meerschaert M.M., Scheffler H.-P., Tadjeran C. Finite difference methods for two-dimensional fractional dispersion equation. J. Comput. Phys. 2006, 211:249-261.
    • (2006) J. Comput. Phys. , vol.211 , pp. 249-261
    • Meerschaert, M.M.1    Scheffler, H.-P.2    Tadjeran, C.3
  • 18
    • 33845628108 scopus 로고    scopus 로고
    • A second-order accurate numerical method for the two-dimensional fractional diffusion equation
    • Tadjeran C., Meerschaert M.M. A second-order accurate numerical method for the two-dimensional fractional diffusion equation. J. Comput. Phys. 2007, 220:813-823.
    • (2007) J. Comput. Phys. , vol.220 , pp. 813-823
    • Tadjeran, C.1    Meerschaert, M.M.2
  • 19
    • 77954142858 scopus 로고    scopus 로고
    • Numerical simulations of 2D fractional subdiffusion problems
    • Brunner H., Ling L., Yamamoto M. Numerical simulations of 2D fractional subdiffusion problems. J. Comput. Phys. 2010, 229:6613-6622.
    • (2010) J. Comput. Phys. , vol.229 , pp. 6613-6622
    • Brunner, H.1    Ling, L.2    Yamamoto, M.3
  • 20
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic differential equations
    • Peaceman D.W., Rachford H.H. The numerical solution of parabolic and elliptic differential equations. J. Soc. Ind. Appl. Math. 1955, 3:28-41.
    • (1955) J. Soc. Ind. Appl. Math. , vol.3 , pp. 28-41
    • Peaceman, D.W.1    Rachford, H.H.2
  • 22
    • 0001742634 scopus 로고
    • A general formulation of alternating direction method. Part I: parabolic and hyperbolic problems
    • Douglas J., Gunn J.E. A general formulation of alternating direction method. Part I: parabolic and hyperbolic problems. Numer. Math. 1964, 6:428-453.
    • (1964) Numer. Math. , vol.6 , pp. 428-453
    • Douglas, J.1    Gunn, J.E.2
  • 23
    • 0012728672 scopus 로고
    • Alternating direction methods for nonlinear time-dependent problems
    • Dendy J.E. Alternating direction methods for nonlinear time-dependent problems. SIAM J. Numer. Anal. 1977, 14:313-326.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 313-326
    • Dendy, J.E.1
  • 25
    • 0004029439 scopus 로고    scopus 로고
    • Implicit, compact, linearized θ-methods with factorization for multidimensional reaction-diffusion equations
    • Ramos J.I. Implicit, compact, linearized θ-methods with factorization for multidimensional reaction-diffusion equations. Appl. Math. Comput. 1998, 94:17-43.
    • (1998) Appl. Math. Comput. , vol.94 , pp. 17-43
    • Ramos, J.I.1
  • 26
    • 0036569404 scopus 로고    scopus 로고
    • An efficient high-order algorithm for solving systems of reaction-diffusion equations
    • Liao W., Zhu J., Khaliq A.Q.M. An efficient high-order algorithm for solving systems of reaction-diffusion equations. Numer. Methods for Partial Differential Eq. 2002, 18:340-354.
    • (2002) Numer. Methods for Partial Differential Eq. , vol.18 , pp. 340-354
    • Liao, W.1    Zhu, J.2    Khaliq, A.Q.M.3
  • 27
    • 54549108683 scopus 로고    scopus 로고
    • A compact alternating direction implicit difference method for reaction diffusion equations
    • (in Chinese)
    • Sun Z.Z., Li X.L. A compact alternating direction implicit difference method for reaction diffusion equations. Math. Numer. Sinica 2005, 27:209-224. (in Chinese).
    • (2005) Math. Numer. Sinica , vol.27 , pp. 209-224
    • Sun, Z.Z.1    Li, X.L.2
  • 28
    • 73449143894 scopus 로고    scopus 로고
    • Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations
    • Liao H.-L., Sun Z.-Z. Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations. Numer. Meth. Partial Differ. Eq. 2010, 26:37-60.
    • (2010) Numer. Meth. Partial Differ. Eq. , vol.26 , pp. 37-60
    • Liao, H.-L.1    Sun, Z.-Z.2
  • 29
    • 77957889961 scopus 로고    scopus 로고
    • High order compact alternating direction implicit method for the generalized sine-Gordon equation
    • Cui M.R. High order compact alternating direction implicit method for the generalized sine-Gordon equation. J. Comput. Appl. Math. 2010, 235:837-849.
    • (2010) J. Comput. Appl. Math. , vol.235 , pp. 837-849
    • Cui, M.R.1
  • 30
    • 84856227286 scopus 로고    scopus 로고
    • Modified alternating direction methds for solving a two-dimensional noncontinuous seepage flow with fractional derivatives
    • in Chinese
    • Liu Q.X., Liu F.W. Modified alternating direction methds for solving a two-dimensional noncontinuous seepage flow with fractional derivatives. Math. Numer. Sinica 2009, 31:179-194. in Chinese.
    • (2009) Math. Numer. Sinica , vol.31 , pp. 179-194
    • Liu, Q.X.1    Liu, F.W.2
  • 31
    • 84860390012 scopus 로고    scopus 로고
    • 2N) alternating-direction finite difference method for two-dimensional fractional diffusion equations
    • 2N) alternating-direction finite difference method for two-dimensional fractional diffusion equations. J. Comput. Phys. 2011, 230:7830-7839.
    • (2011) J. Comput. Phys. , vol.230 , pp. 7830-7839
    • Wang, H.1    Wang, K.X.2
  • 32
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • Lubich C. Discretized fractional calculus. SIAM J. Math. Anal. 1986, 17(3):704-719.
    • (1986) SIAM J. Math. Anal. , vol.17 , Issue.3 , pp. 704-719
    • Lubich, C.1
  • 33
    • 77955927812 scopus 로고    scopus 로고
    • 2N) finite difference method for fractional diffusion equations
    • 2N) finite difference method for fractional diffusion equations. J. Comput. Phys. 2010, 229:8095-8104.
    • (2010) J. Comput. Phys. , vol.229 , pp. 8095-8104
    • Wang, H.1    Wang, K.X.2    Sircar, T.3
  • 34
    • 0003423678 scopus 로고
    • Numerical Partial Differential Equations: Finite Difference Methods
    • Springer-Verlag
    • Thomas J.W. Numerical Partial Differential Equations: Finite Difference Methods. Texts in Applied Mathematics 1995, Vol. 22. Springer-Verlag.
    • (1995) Texts in Applied Mathematics , vol.22
    • Thomas, J.W.1
  • 35
    • 36149001420 scopus 로고    scopus 로고
    • A Fourier method for the fractional diffusion equation describing sub-diffusion
    • Chen C.M., Liu F.W., Turner I., Anh V. A Fourier method for the fractional diffusion equation describing sub-diffusion. J. Comput. Phys. 2007, 227:886-897.
    • (2007) J. Comput. Phys. , vol.227 , pp. 886-897
    • Chen, C.M.1    Liu, F.W.2    Turner, I.3    Anh, V.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.