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Volumn 4, Issue PART B, 2010, Pages 1015-1024

Stability and convergence of two new implicit numerical methods for the fractional cable equation

Author keywords

[No Author keywords available]

Indexed keywords

CABLE EQUATION; CONVERGENCE ORDER; ENERGY METHOD; FRACTIONAL ORDER; FUNDAMENTAL EQUATIONS; IMPLICIT NUMERICAL METHOD; NEURONAL DYNAMICS; NUMERICAL RESULTS; PARTIAL DERIVATIVES; STABILITY AND CONVERGENCE; SUBDIFFUSION; TEMPORAL DERIVATIVES; TEMPORAL OPERATORS; TIME AND SPACE;

EID: 77953719945     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC2009-86578     Document Type: Conference Paper
Times cited : (4)

References (22)
  • 1
    • 0024367526 scopus 로고
    • An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites, spines and axons
    • Qian, N., and Sejnowski, T., 1989. An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites, spines and axons. Biol. Cybern., 62, pp. 1-15.
    • (1989) Biol. Cybern. , vol.62 , pp. 1-15
    • Qian, N.1    Sejnowski, T.2
  • 2
    • 0034805503 scopus 로고    scopus 로고
    • Anomalous subdiffusion in fluorescence photobleaching recovery: A monte carlo study
    • Saxton, M., 2001. Anomalous subdiffusion in fluorescence photobleaching recovery: A monte carlo study. Biophys. J., 81, pp. 2226-2240.
    • (2001) Biophys. J. , vol.81 , pp. 2226-2240
    • Saxton, M.1
  • 5
    • 33751019968 scopus 로고    scopus 로고
    • Anomalous diffusion in Purkinje cell dendrites caused by spines
    • Santamaria, F., Wils, S., De Schutter, E., and Augustine, G.J., 2006. Anomalous Diffusion in Purkinje Cell Dendrites Caused by Spines. Neuron, 52, pp. 635-648.
    • (2006) Neuron , vol.52 , pp. 635-648
    • Santamaria, F.1    Wils, S.2    De Schutter, E.3    Augustine, G.J.4
  • 6
    • 41549083671 scopus 로고    scopus 로고
    • Fractional cable models for spiny neuronal dendrites
    • Henry, B.I., Langlands, T.A.M., and Wearne, S.L., 2008. Fractional Cable Models for Spiny Neuronal Dendrites. Phys. Rev. Lett., 100, pp. 128103.
    • (2008) Phys. Rev. Lett. , vol.100 , pp. 128103
    • Henry, B.I.1    Langlands, T.A.M.2    Wearne, S.L.3
  • 7
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of the space fractional Fokker-Planck equation
    • Liu, F., Anh, V., and Turner, I., 2004. Numerical Solution of the Space Fractional Fokker-Planck Equation. J. Comp. Appl. Math., 166, pp. 209-219.
    • (2004) J. Comp. Appl. Math. , vol.166 , pp. 209-219
    • Liu, F.1    Anh, V.2    Turner, I.3
  • 8
    • 4444368867 scopus 로고    scopus 로고
    • Finite difference approximations for fractional advection-dispersion flow equations
    • Meerschaert, M., and Tadjeran, C., 2004. Finite difference approximations for fractional advection-dispersion flow equations. J. Comp. Appl. Math., 172, pp. 65-77.
    • (2004) J. Comp. Appl. Math. , vol.172 , pp. 65-77
    • Meerschaert, M.1    Tadjeran, C.2
  • 9
    • 33646191893 scopus 로고    scopus 로고
    • Computational aspects of FEM approximation of fractional advection dispersion equation on bounded domains in R2
    • Roop, J.P., 2006. Computational aspects of FEM approximation of fractional advection dispersion equation on bounded domains in R2. J. Comp. Appl. Math., 193, pp. 243-268.
    • (2006) J. Comp. Appl. Math. , vol.193 , pp. 243-268
    • Roop, J.P.1
  • 10
    • 33751545053 scopus 로고    scopus 로고
    • Fractional high order methods for the nonlinear fractional ordinary differential equation
    • Lin, R., and Liu, F., 2007. Fractional high order methods for the nonlinear fractional ordinary differential equation. Nonlinear Analysis, 66, pp. 856-869.
    • (2007) Nonlinear Analysis , vol.66 , pp. 856-869
    • Lin, R.1    Liu, F.2
  • 11
    • 33846798041 scopus 로고    scopus 로고
    • Approximation of the Levy-Feller advection-dispersion process by random walk and finite difference method
    • Liu, Q., Liu, F., Turner, I., and Anh, V., 2007. Approximation of the Levy-Feller advection-dispersion process by random walk and finite difference method. J. Phys. Comp., 222, pp. 57-70.
    • (2007) J. Phys. Comp. , vol.222 , pp. 57-70
    • Liu, Q.1    Liu, F.2    Turner, I.3    Anh, V.4
  • 12
    • 84907893973 scopus 로고    scopus 로고
    • Numerical methods f or the variable-order fractional advection- diffusiion with a nonlinear source term
    • in press, (doi: 10.1137/080730597)
    • Zhuang, P., Liu, F., Anh, V., and Turner, I., 2009. Numerical methods f or the variable-order fractional advection- diffusiion with a nonlinear source term, SIAM J. on Numerical Analysis, in press, (doi: 10.1137/080730597).
    • (2009) SIAM J. on Numerical Analysis
    • Zhuang, P.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 13
    • 67349098149 scopus 로고    scopus 로고
    • Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
    • in press, (doi: 10.1016/j.amc.2009.02.047)
    • Lin, R., Liu, F., Anh, V., and Turner, I., 2009. Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation, Applied and Computational Mathematics, in press, (doi: 10.1016/j.amc.2009.02.047).
    • (2009) Applied and Computational Mathematics
    • Lin, R.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 14
    • 41449094744 scopus 로고    scopus 로고
    • Solving linear and nonlinear space-time fractional reaction-diffusion equations by Adomian decomposition method
    • Yu, Q., Liu, F., Anh, V., and Turner, I., 2008. Solving linear and nonlinear space-time fractional reaction-diffusion equations by Adomian decomposition method. International J. for Numer. Meth. In Eng., 74, pp. 138-158.
    • (2008) International J. for Numer. Meth. in Eng. , vol.74 , pp. 138-158
    • Yu, Q.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 15
    • 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., 2005. An explicit finite difference method and a new Von Neumann-type stability analysis for fractional diffusion equations. SIAM J. Numer. Anal., 42(5), pp. 1862-1874.
    • (2005) SIAM J. Numer. Anal. , vol.42 , Issue.5 , pp. 1862-1874
    • Yuste, S.B.1    Acedo, L.2
  • 16
    • 33646128485 scopus 로고    scopus 로고
    • Weighted average finite difference methods for fractional diffusion equations
    • Yuste, S.B., 2006. Weighted average finite difference methods for fractional diffusion equations. J. Comp. Phys., 216(1), pp. 264-274.
    • (2006) J. Comp. Phys. , vol.216 , Issue.1 , pp. 264-274
    • Yuste, S.B.1
  • 17
    • 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., 2005. The accuracy and stability of an implicit solution method for the fractional diffusion equation. J. Comp. Phys., 205, pp. 719- 736.
    • (2005) J. Comp. Phys. , vol.205 , pp. 719-736
    • Langlands, T.A.M.1    Henry, B.I.2
  • 18
    • 36149001420 scopus 로고    scopus 로고
    • Fourier method for the fractional diffusion equation describing sub-diffusion
    • Chen, C., Liu, F., Turner, I., and Anh, V., 2007. Fourier method for the fractional diffusion equation describing sub-diffusion. J. Comp. Phys., 227, pp. 886-897.
    • (2007) J. Comp. Phys. , vol.227 , pp. 886-897
    • Chen, C.1    Liu, F.2    Turner, I.3    Anh, V.4
  • 19
    • 56949093590 scopus 로고    scopus 로고
    • A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative
    • doi: 10.1016/j.cam.2008.03.01
    • Chen, C., Liu F., and Anh, V., 2009. A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative, J. Comp. Appl. Math., 223, pp.777-789, (doi: 10.1016/j.cam.2008.03.01).
    • (2009) J. Comp. Appl. Math. , vol.223 , pp. 777-789
    • Chen, C.1    Liu, F.2    Anh, V.3
  • 20
    • 55549107511 scopus 로고    scopus 로고
    • New solution and analytical techniques of the implicit numerical methods for the anomalous sub-diffusion equation
    • Zhuang, P., Liu, F., Anh, V., and Turner, I., 2008. New solution and analytical techniques of the implicit numerical methods for the anomalous sub-diffusion equation SIAM J. on Numerical Analysis, 46(2), pp. 1079-1095.
    • (2008) SIAM J. on Numerical Analysis , vol.46 , Issue.2 , pp. 1079-1095
    • Zhuang, P.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 21
    • 67349231192 scopus 로고    scopus 로고
    • Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term
    • in press
    • Liu, F., Yang, C., and Burrage, K., 2009. Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term. Journal of Computational and Applied Mathematics, in press.
    • (2009) Journal of Computational and Applied Mathematics
    • Liu, F.1    Yang, C.2    Burrage, K.3


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