Nonsmooth data error estimates for FEM approximations of the time fractional cable equation

[1]  C. Lubich.  Convolution quadrature and discretized operational calculus. II , 1988 .

[2]  Vidar Thomée,et al.  Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term , 1996, Math. Comput..

[3]  I. Podlubny.  Fractional differential equations , 1998 .

[4]  Eduardo Cuesta,et al.  Convolution quadrature time discretization of fractional diffusion-wave equations , 2006, Math. Comput..

[5]  S. Wearne,et al.  Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions , 2009, Journal of mathematical biology.

[6]  W. McLean.  Regularity of solutions to a time-fractional diffusion equation , 2010 .

[7]  S. B. Yuste,et al.  An Explicit Numerical Method for the Fractional Cable Equation , 2011 .

[8]  I. Turner,et al.  Two New Implicit Numerical Methods for the Fractional Cable Equation , 2011 .

[9]  Bruce Ian Henry,et al.  Fractional Cable Equation Models for Anomalous Electrodiffusion in Nerve Cells: Finite Domain Solutions , 2011, SIAM J. Appl. Math..

[10]  Xianjuan Li,et al.  Finite difference/spectral approximations for the fractional cable equation , 2010, Math. Comput..

[11]  Lu-ming Zhang,et al.  Implicit compact difference schemes for the fractional cable equation , 2012 .

[12]  Zhibo Wang,et al.  Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation , 2013, J. Comput. Phys..

[13]  Xuli Han,et al.  Discrete-time orthogonal spline collocation method with application to two-dimensional fractional cable equation , 2014, Comput. Math. Appl..

[14]  Hong Li,et al.  A two-grid finite element approximation for a nonlinear time-fractional Cable equation , 2015, 1512.08082.

[15]  Roberto Garrappa,et al.  Numerical Evaluation of Two and Three Parameter Mittag-Leffler Functions , 2015, SIAM J. Numer. Anal..

[16]  William McLean,et al.  Time-stepping error bounds for fractional diffusion problems with non-smooth initial data , 2014, J. Comput. Phys..

[17]  Bangti Jin,et al.  An analysis of the Rayleigh–Stokes problem for a generalized second-grade fluid , 2014, Numerische Mathematik.

[18]  Fawang Liu,et al.  Galerkin finite element method and error analysis for the fractional cable equation , 2015, Numerical Algorithms.

[19]  Han Zhou,et al.  A class of second order difference approximations for solving space fractional diffusion equations , 2012, Math. Comput..

[20]  Hong Li,et al.  A new fully discrete finite difference/element approximation for fractional cable equation , 2016 .

[21]  Bo Yu,et al.  Numerical Identification of the Fractional Derivatives in the Two-Dimensional Fractional Cable Equation , 2016, J. Sci. Comput..

[22]  Bangti Jin,et al.  Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data , 2016, SIAM J. Sci. Comput..

[23]  Z. Zhao,et al.  The discontinuous Galerkin finite element method for fractional cable equation , 2017 .