메뉴 건너뛰기




Volumn 5, Issue 2, 2014, Pages 253-259

Numerical simulation of fractional Cable equation of spiny neuronal dendrites

Author keywords

Fractional Cable equation; John von Neumann stability analysis; Weighted average finite difference approximations

Indexed keywords


EID: 84897605207     PISSN: 20901232     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jare.2013.03.006     Document Type: Article
Times cited : (39)

References (24)
  • 1
    • 41549083671 scopus 로고    scopus 로고
    • Fractional Cable models for spiny neuronal dendrites
    • [Article ID 128103]
    • Henry B.I., Langlands T.A.M., Wearne S.L. Fractional Cable models for spiny neuronal dendrites. Phys Rev Lett 2008, 100(12):4. [Article ID 128103].
    • (2008) Phys Rev Lett , vol.100 , Issue.12 , pp. 4
    • Henry, B.I.1    Langlands, T.A.M.2    Wearne, S.L.3
  • 3
    • 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
  • 5
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • Lubich C. Discretized fractional calculus. SIAM J Math Anal 1986, 17:704-719.
    • (1986) SIAM J Math Anal , vol.17 , pp. 704-719
    • Lubich, C.1
  • 8
    • 35349007940 scopus 로고    scopus 로고
    • Numerical studies for a multi-order fractional differential equation
    • Sweilam N.H., Khader M.M., Al-Bar R.F. Numerical studies for a multi-order fractional differential equation. Phys Lett A 2007, 371:26-33.
    • (2007) Phys Lett A , vol.371 , pp. 26-33
    • Sweilam, N.H.1    Khader, M.M.2    Al-Bar, R.F.3
  • 9
    • 79251601340 scopus 로고    scopus 로고
    • Numerical solution of two-sided space-fractional wave equation using finite difference method
    • Sweilam N.H., Khader M.M., Nagy A.M. Numerical solution of two-sided space-fractional wave equation using finite difference method. J Comput Appl Math 2011, 235:2832-2841.
    • (2011) J Comput Appl Math , vol.235 , pp. 2832-2841
    • Sweilam, N.H.1    Khader, M.M.2    Nagy, A.M.3
  • 10
    • 84872599320 scopus 로고    scopus 로고
    • On the stability analysis of weighted average finite difference methods for fractional wave equation
    • Sweilam N.H., Khader M.M., Adel M. On the stability analysis of weighted average finite difference methods for fractional wave equation. J Fract Differential Cal 2012, 2(2):17-25.
    • (2012) J Fract Differential Cal , vol.2 , Issue.2 , pp. 17-25
    • Sweilam, N.H.1    Khader, M.M.2    Adel, M.3
  • 11
    • 85162538951 scopus 로고    scopus 로고
    • Crank-Nicolson finite difference method for solving time-fractional diffusion equation
    • Sweilam N.H., Khader M.M., Mahdy A.M.S. Crank-Nicolson finite difference method for solving time-fractional diffusion equation. J Fract Cal Appl 2012, 2(2):1-9.
    • (2012) J Fract Cal Appl , vol.2 , Issue.2 , pp. 1-9
    • Sweilam, N.H.1    Khader, M.M.2    Mahdy, A.M.S.3
  • 12
    • 79960376707 scopus 로고    scopus 로고
    • A Chebyshev pseudo-spectral method for solving fractional order integro-differential equations
    • Sweilam N.H., Khader M.M. A Chebyshev pseudo-spectral method for solving fractional order integro-differential equations. ANZIAM 2010, 51:464-475.
    • (2010) ANZIAM , vol.51 , pp. 464-475
    • Sweilam, N.H.1    Khader, M.M.2
  • 13
    • 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, 42:1862-1874.
    • (2005) SIAM J Numer Anal , vol.42 , pp. 1862-1874
    • Yuste, S.B.1    Acedo, L.2
  • 14
    • 0026124343 scopus 로고    scopus 로고
    • Fractional-order state equations for the control of viscoelastic damped structures
    • Bagley R.L., Calico R.A. Fractional-order state equations for the control of viscoelastic damped structures. J Guid Control Dyn 1999, 14(2):304-311.
    • (1999) J Guid Control Dyn , vol.14 , Issue.2 , pp. 304-311
    • Bagley, R.L.1    Calico, R.A.2
  • 16
    • 0034113992 scopus 로고    scopus 로고
    • The fractional-order governing equation of Le'vy motion
    • Benson D.A., Wheatcraft S.W., Meerschaert M.M. The fractional-order governing equation of Le'vy motion. Water Resour Res 2000, 36(6):1413-1424.
    • (2000) Water Resour Res , vol.36 , Issue.6 , pp. 1413-1424
    • Benson, D.A.1    Wheatcraft, S.W.2    Meerschaert, M.M.3
  • 17
    • 79959753668 scopus 로고    scopus 로고
    • Image processing by means of a linear integro-differential equations
    • Cuesta E., Finat J. Image processing by means of a linear integro-differential equations. IASTED 2003, 438-442.
    • (2003) IASTED , pp. 438-442
    • Cuesta, E.1    Finat, J.2
  • 19
    • 70350663279 scopus 로고    scopus 로고
    • Fractional Cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions
    • Langlands T.A.M., Henry B.I., Wearne S.L. Fractional Cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions. J Math Biol 2009, 59(6):761-808.
    • (2009) J Math Biol , vol.59 , Issue.6 , pp. 761-808
    • Langlands, T.A.M.1    Henry, B.I.2    Wearne, S.L.3
  • 20
    • 78649919287 scopus 로고    scopus 로고
    • Stability and convergence of two new implicit numerical methods for the fractional Cable equation
    • [Article ID 01109]
    • Liu F., Yang Q., Turner I. Stability and convergence of two new implicit numerical methods for the fractional Cable equation. J Comput Nonlinear Dyn 2011, 6(1):7. [Article ID 01109].
    • (2011) J Comput Nonlinear Dyn , vol.6 , Issue.1 , pp. 7
    • Liu, F.1    Yang, Q.2    Turner, I.3
  • 21
    • 84878576090 scopus 로고    scopus 로고
    • An explicit numerical method for the fractional Cable equation
    • [Article ID 231920]
    • Quintana-Murillo J., Yuste S.B. An explicit numerical method for the fractional Cable equation. Int J Differential Equations 2011, 2011:12. [Article ID 231920].
    • (2011) Int J Differential Equations , vol.2011 , pp. 12
    • Quintana-Murillo, J.1    Yuste, S.B.2
  • 22
    • 0003089278 scopus 로고
    • Core conductor theory and Cable properties of neurons
    • American Physiological Society, Bethesda (MD), [chapter 3]
    • Rall W. Core conductor theory and Cable properties of neurons. Handbook of physiology:the nervous system 1977, vol. 1:39-97. American Physiological Society, Bethesda (MD), [chapter 3].
    • (1977) Handbook of physiology:the nervous system , vol.1 , pp. 39-97
    • Rall, W.1
  • 24
    • 4544380424 scopus 로고    scopus 로고
    • A numerical method for an integro-differential equation with memory in Banach spaces: qualitative properties
    • Palencia E., Cuesta E. A numerical method for an integro-differential equation with memory in Banach spaces: qualitative properties. SIAM J Numer Anal 2003, 41:1232-1241.
    • (2003) SIAM J Numer Anal , vol.41 , pp. 1232-1241
    • Palencia, E.1    Cuesta, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.