메뉴 건너뛰기




Volumn 2011, Issue , 2011, Pages

An explicit numerical method for the fractional cable equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84878576090     PISSN: 16879643     EISSN: 16879651     Source Type: Journal    
DOI: 10.1155/2011/231920     Document Type: Article
Times cited : (29)

References (42)
  • 5
    • 38349041965 scopus 로고    scopus 로고
    • Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation
    • R. L. Magin, O. Abdullah, D. Baleanu, and X. J. Zhou, "Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation," Journal of Magnetic Resonance, vol. 190, no. 2, pp. 255-270, 2008.
    • (2008) Journal of Magnetic Resonance , vol.190 , Issue.2 , pp. 255-270
    • Magin, R.L.1    Abdullah, O.2    Baleanu, D.3    Zhou, X.J.4
  • 6
    • 77952842666 scopus 로고    scopus 로고
    • Fractional variational principles in action
    • Article ID 014006
    • D. Baleanu, "Fractional variational principles in action," Physica Scripta, vol. 2009, no. T136, Article ID 014006, 4 pages, 2009.
    • (2009) Physica Scripta , vol.2009 , Issue.T136 , pp. 4
    • Baleanu, D.1
  • 7
    • 1642632896 scopus 로고    scopus 로고
    • Some exact results for the trapping of subdiffusive particles in one dimension
    • S. B. Yuste and L. Acedo, "Some exact results for the trapping of subdiffusive particles in one dimension," Physica A, vol. 336, no. 3-4, pp. 334-346, 2004.
    • (2004) Physica A , vol.336 , Issue.3-4 , pp. 334-346
    • Yuste, S.B.1    Acedo, L.2
  • 8
    • 33244460273 scopus 로고    scopus 로고
    • Trapping reactionswith subdiffusive traps and particles characterized by different anomalous diffusion exponents
    • Article ID 061103
    • S. B. Yuste and K. Lindenberg, "Trapping reactionswith subdiffusive traps and particles characterized by different anomalous diffusion exponents," Physical Review E, vol. 72, no. 6, Article ID 061103, 8 pages, 2005.
    • (2005) Physical Review e , vol.72 , Issue.6 , pp. 8
    • Yuste, S.B.1    Lindenberg, K.2
  • 9
    • 36249022599 scopus 로고    scopus 로고
    • Subdiffusive target problem: Survival probability
    • Article ID 051114
    • S. B. Yuste and K. Lindenberg, "Subdiffusive target problem: survival probability," Physical Review E, vol. 76, no. 5, Article ID 051114, 6 pages, 2007.
    • (2007) Physical Review e , vol.76 , Issue.5 , pp. 6
    • Yuste, S.B.1    Lindenberg, K.2
  • 10
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler and J. Klafter, "The random walk's guide to anomalous diffusion: a fractional dynamics approach," Physics Reports, vol. 339, no. 1, p. 77, 2000.
    • (2000) Physics Reports , vol.339 , Issue.1 , pp. 77
    • Metzler, R.1    Klafter, J.2
  • 11
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics
    • R. Metzler and J. Klafter, "The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics," Journal of Physics A, vol. 37, no. 31, pp. R161-R208, 2004.
    • (2004) Journal of Physics A , vol.37 , Issue.31
    • Metzler, R.1    Klafter, J.2
  • 12
    • 18144408075 scopus 로고    scopus 로고
    • Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker-Planck equation approach
    • R. Metzler, E. Barkai, and J. Klafter, "Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker-Planck equation approach," Physical Review Letters, vol. 82, no. 18, pp. 3563-3567, 1999.
    • (1999) Physical Review Letters , vol.82 , Issue.18 , pp. 3563-3567
    • Metzler, R.1    Barkai, E.2    Klafter, J.3
  • 13
    • 78651468385 scopus 로고    scopus 로고
    • A reaction-subdiffusion model of morphogen gradient formation
    • Article ID 061123
    • S. B. Yuste, E. Abad, and K. Lindenberg, "A reaction-subdiffusion model of morphogen gradient formation," Physical Review E, vol. 82, no. 6, Article ID 061123, 9 pages, 2010.
    • (2010) Physical Review e , vol.82 , Issue.6 , pp. 9
    • Yuste, S.B.1    Abad, E.2    Lindenberg, K.3
  • 14
    • 48249124302 scopus 로고    scopus 로고
    • Crowding effects on diffusion in solutions and cells
    • J. A. Dix and A. S. Verkman, "Crowding effects on diffusion in solutions and cells," Annual Review of Biophysics, vol. 37, pp. 247-263, 2008.
    • (2008) Annual Review of Biophysics , vol.37 , pp. 247-263
    • Dix, J.A.1    Verkman, A.S.2
  • 15
    • 2942551253 scopus 로고    scopus 로고
    • Anomalous Diffusion Probes Microstructure Dynamics of Entangled F-Actin Networks
    • Article ID 178101
    • I. Y. Wong, M. L. Gardel, D. R. Reichman et al., "Anomalous Diffusion Probes Microstructure Dynamics of Entangled F-Actin Networks," Physical Review Letters, vol. 92, no. 17, Article ID 178101, 4 pages, 2004.
    • (2004) Physical Review Letters , vol.92 , Issue.17 , pp. 4
    • Wong, I.Y.1    Gardel, M.L.2    Reichman Et Al., D.R.3
  • 16
    • 79251477200 scopus 로고    scopus 로고
    • In Vivo Anomalous Diffusion andWeak Ergodicity Breaking of Lipid Granules
    • Article ID 048103
    • J.-H. Jeon, V. Tejedor, S. Burov et al., "In Vivo Anomalous Diffusion andWeak Ergodicity Breaking of Lipid Granules," Physical Review Letters, vol. 106, no. 4, Article ID 048103, 4 pages, 2011.
    • (2011) Physical Review Letters , vol.106 , Issue.4 , pp. 4
    • Jeon, J.-H.1    Tejedor, V.2    Burov Et Al., S.3
  • 17
    • 70350663279 scopus 로고    scopus 로고
    • Fractional cable equation models for anomalous electrodiffusion in nerve cells: Infinite domain solutions
    • T. A. M. Langlands, B. I. Henry, and S. L. Wearne, "Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions," Journal of Mathematical Biology, vol. 59, no. 6, pp. 761-808, 2009.
    • (2009) Journal of Mathematical Biology , vol.59 , Issue.6 , pp. 761-808
    • Langlands, T.A.M.1    Henry, B.I.2    Wearne, S.L.3
  • 18
    • 41549083671 scopus 로고    scopus 로고
    • Fractional cable models for spiny neuronal dendrites
    • Article ID 128103
    • B. I. Henry, T. A. M. Langlands, and S. L. Wearne, "Fractional cable models for spiny neuronal dendrites," Physical Review Letters, vol. 100, no. 12, Article ID 128103, p. 4, 2008.
    • (2008) Physical Review Letters , vol.100 , Issue.12 , pp. 4
    • Henry, B.I.1    Langlands, T.A.M.2    Wearne, S.L.3
  • 19
    • 0041107241 scopus 로고    scopus 로고
    • The generalized Cattaneo equation for the description of anomalous transport processes
    • A. Compte and R. Metzler, "The generalized Cattaneo equation for the description of anomalous transport processes," Journal of Physics A, vol. 30, no. 21, pp. 7277-7289, 1997.
    • (1997) Journal of Physics A , vol.30 , Issue.21 , pp. 7277-7289
    • Compte, A.1    Metzler, R.2
  • 20
    • 0000237249 scopus 로고    scopus 로고
    • Fractional diffusion, waiting-time distributions, and Cattaneotype equations
    • R. Metzler and T. F. Nonnenmacher, "Fractional diffusion, waiting-time distributions, and Cattaneotype equations," Physical Review E, vol. 57, no. 6, pp. 6409-6414, 1998.
    • (1998) Physical Review e , vol.57 , Issue.6 , pp. 6409-6414
    • Metzler, R.1    Nonnenmacher, T.F.2
  • 21
    • 33947692255 scopus 로고    scopus 로고
    • Exact solutions for time-fractional diffusion-wave equations by decomposition method
    • S. S. Ray, "Exact solutions for time-fractional diffusion-wave equations by decomposition method," Physica Scripta, vol. 75, no. 1, pp. 53-61, 2007.
    • (2007) Physica Scripta , vol.75 , Issue.1 , pp. 53-61
    • Ray, S.S.1
  • 22
    • 35349007529 scopus 로고    scopus 로고
    • Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation
    • S. Momani, A. Odibat, and V. S. Erturk, "Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation," Physics Letters. A, vol. 370, no. 5-6, pp. 379-387, 2007.
    • (2007) Physics Letters. A , vol.370 , Issue.5-6 , pp. 379-387
    • Momani, S.1    Odibat, A.2    Erturk, V.S.3
  • 23
    • 35348938590 scopus 로고    scopus 로고
    • Solving fractional diffusion and wave equations by modified homotopy perturbation method
    • H. Jafari and S. Momani, "Solving fractional diffusion and wave equations by modified homotopy perturbation method," Physics Letters. A, vol. 370, no. 5-6, pp. 388-396, 2007.
    • (2007) Physics Letters. A , vol.370 , Issue.5-6 , pp. 388-396
    • Jafari, H.1    Momani, S.2
  • 24
    • 33748901201 scopus 로고    scopus 로고
    • The Adomian decomposition method for solving partial differential equations of fractal order in finite domains
    • A. M. A. El-Sayed and M. Gaber, "The Adomian decomposition method for solving partial differential equations of fractal order in finite domains," Physics Letters A, vol. 359, no. 3, pp. 175-182, 2006.
    • (2006) Physics Letters A , vol.359 , Issue.3 , pp. 175-182
    • El-Sayed, A.M.A.1    Gaber, M.2
  • 25
    • 61349186917 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus. II. Partial fractional differential equations
    • I. Podlubny, A. V. Chechkin, T. Skovranek, Y. Chen, and B. M. Vinagre Jara, "Matrix approach to discrete fractional calculus. II. Partial fractional differential equations," Journal of Computational Physics, vol. 228, no. 8, pp. 3137-3153, 2009.
    • (2009) Journal of Computational Physics , vol.228 , Issue.8 , pp. 3137-3153
    • Podlubny, I.1    Chechkin, A.V.2    Skovranek, T.3    Chen, Y.4    Vinagre Jara, B.M.5
  • 26
    • 0035305938 scopus 로고    scopus 로고
    • Fractional Fokker-Planck equation, solution, and application
    • Article ID 046118
    • E. Barkai, "Fractional Fokker-Planck equation, solution, and application," Physical Review E, vol. 63, no. 4, Article ID 046118, 17 pages, 2001.
    • (2001) Physical Review e , vol.63 , Issue.4 , pp. 17
    • Barkai, E.1
  • 27
    • 0032654412 scopus 로고    scopus 로고
    • Time domain modeling of damping using anelastic displacement fields and fractional calculus
    • M. Enelund and G. A. Lesieutre, "Time domain modeling of damping using anelastic displacement fields and fractional calculus," International Journal of Solids and Structures, vol. 36, no. 29, pp. 4447-4472, 1999.
    • (1999) International Journal of Solids and Structures , vol.36 , Issue.29 , pp. 4447-4472
    • Enelund, M.1    Lesieutre, G.A.2
  • 28
    • 14644446063 scopus 로고    scopus 로고
    • Least squares finite-element solution of a fractional order two-point boundary value problem
    • G. J. Fix and J. P. Roop, "Least squares finite-element solution of a fractional order two-point boundary value problem," Computers & Mathematics with Applications. An International Journal, vol. 48, no. 7-8, pp. 1017-1033, 2004.
    • (2004) Computers & Mathematics with Applications. An International Journal , vol.48 , Issue.7-8 , pp. 1017-1033
    • Fix, G.J.1    Roop, J.P.2
  • 29
    • 76449122108 scopus 로고    scopus 로고
    • A note on the finite element method for the space-fractional advection diffusion equation
    • Y. Zheng, C. Li, and Z. Zhao, "A note on the finite element method for the space-fractional advection diffusion equation," Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1718-1726, 2010.
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.5 , pp. 1718-1726
    • Zheng, Y.1    Li, C.2    Zhao, Z.3
  • 30
    • 79251585926 scopus 로고    scopus 로고
    • A fully discrete discontinuous Galerkinmethod for nonlinear fractional Fokker-Planck equation
    • Article ID 279038
    • Y. Zheng, C. Li, and Z. Zhao, "A fully discrete discontinuous Galerkinmethod for nonlinear fractional Fokker-Planck equation," Mathematical Problems in Engineering, vol. 2010, Article ID 279038, p. 26, 2010.
    • (2010) Mathematical Problems in Engineering , vol.2010 , pp. 26
    • Zheng, Y.1    Li, C.2    Zhao, Z.3
  • 31
    • 0036650850 scopus 로고    scopus 로고
    • Time fractional diffusion: A discrete random walk approach
    • R. Gorenflo, F. Mainardi, D. Moretti, and P. Paradisi, "Time fractional diffusion: a discrete random walk approach," Nonlinear Dynamics, vol. 29, no. 1-4, pp. 129-143, 2002.
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 129-143
    • Gorenflo, R.1    Mainardi, F.2    Moretti, D.3    Paradisi, P.4
  • 32
    • 25444472344 scopus 로고    scopus 로고
    • An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations
    • S. B. Yuste and L. Acedo, "An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations," SIAM Journal on Numerical Analysis, vol. 42, no. 5, pp. 1862-1874, 2005.
    • (2005) SIAM Journal on Numerical Analysis , vol.42 , Issue.5 , pp. 1862-1874
    • Yuste, S.B.1    Acedo, L.2
  • 33
    • 85015137309 scopus 로고    scopus 로고
    • On three explicit difference schemes for fractional diffusion and diffusion-wave equations
    • Article ID 014025
    • S. B. Yuste and J. Quintana-Murillo, "On three explicit difference schemes for fractional diffusion and diffusion-wave equations," Physica Scripta, vol. 2009, no. T136, Article ID 014025, 6 pages, 2009.
    • (2009) Physica Scripta , vol.2009 , Issue.T136 , pp. 6
    • Yuste, S.B.1    Quintana-Murillo, J.2
  • 34
    • 33646128485 scopus 로고    scopus 로고
    • Weighted average finite difference methods for fractional diffusion equations
    • S. B. Yuste, "Weighted average finite difference methods for fractional diffusion equations," Journal of Computational Physics, vol. 216, no. 1, pp. 264-274, 2006.
    • (2006) Journal of Computational Physics , vol.216 , Issue.1 , pp. 264-274
    • Yuste, S.B.1
  • 35
    • 78649924907 scopus 로고    scopus 로고
    • An explicit difference method for solving fractional diffusion and diffusion-wave equations in the Caputo form
    • Article ID 021014
    • J. Quintana-Murillo and S. B. Yuste, "An explicit difference method for solving fractional diffusion and diffusion-wave equations in the Caputo form," Journal of Computational and Nonlinear Dynamics, vol. 6, no. 2, Article ID 021014, 6 pages, 2011.
    • (2011) Journal of Computational and Nonlinear Dynamics , vol.6 , Issue.2 , pp. 6
    • Quintana-Murillo, J.1    Yuste, S.B.2
  • 36
    • 36149001420 scopus 로고    scopus 로고
    • A Fourier method for the fractional diffusion equation describing sub-diffusion
    • C. M. Chen, F. Liu, I. Turner, and V. Anh, "A Fourier method for the fractional diffusion equation describing sub-diffusion," Journal of Computational Physics, vol. 227, no. 2, pp. 886-897, 2007.
    • (2007) Journal of Computational Physics , vol.227 , Issue.2 , pp. 886-897
    • Chen, C.M.1    Liu, F.2    Turner, I.3    Anh, V.4
  • 37
    • 55549107511 scopus 로고    scopus 로고
    • New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation
    • P. Zhuang, F. Liu, V. Anh, and I. Turner, "New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation," SIAM Journal on Numerical Analysis, vol. 46, no. 2, pp. 1079-1095, 2008.
    • (2008) SIAM Journal on Numerical Analysis , vol.46 , Issue.2 , pp. 1079-1095
    • Zhuang, P.1    Liu, F.2    Anh, V.3    Turner, I.4
  • 38
    • 78649919287 scopus 로고    scopus 로고
    • Stability and convergence of two new implicit numerical methods for the fractional cable equation
    • Article ID 01109
    • F. Liu, Q. Yang, and I. Turner, "Stability and convergence of two new implicit numerical methods for the fractional cable equation," Journal of Computational and Nonlinear Dynamics, vol. 6, no. 1, Article ID 01109, 7 pages, 2011.
    • (2011) Journal of Computational and Nonlinear Dynamics , vol.6 , Issue.1 , pp. 7
    • Liu, F.1    Yang, Q.2    Turner, I.3
  • 40
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • Ch. Lubich, "Discretized fractional calculus," SIAM Journal on Mathematical Analysis, vol. 17, no. 3, pp. 704-719, 1986.
    • (1986) SIAM Journal on Mathematical Analysis , vol.17 , Issue.3 , pp. 704-719
    • Lubich, Ch.1
  • 42
    • 69049086472 scopus 로고    scopus 로고
    • Compact finite difference method for the fractional diffusion equation
    • M. Cui, "Compact finite difference method for the fractional diffusion equation," Journal of Computational Physics, vol. 228, no. 20, pp. 7792-7804, 2009.
    • (2009) Journal of Computational Physics , vol.228 , Issue.20 , pp. 7792-7804
    • Cui, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.