TY - EJOU AU - Wang, Zhen TI - On Caputo-Type Cable Equation: Analysis and Computation T2 - Computer Modeling in Engineering \& Sciences PY - 2020 VL - 123 IS - 1 SN - 1526-1506 AB - In this paper, a special case of nonlinear time fractional cable equation is studied. For the equation defined on a bounded domain, the existence, uniqueness, and regularity of the solution are firstly studied. Furthermore, it is numerically studied via the weighted and shifted Grünwald difference (WSGD) methods/the local discontinuous Galerkin (LDG) finite element methods. The derived numerical scheme has been proved to be stable and convergent with order O(∆t2 + hk+1), where ∆t, h, k are the time stepsize, the spatial stepsize, and the degree of piecewise polynomials, respectively. Finally, a numerical experiment is presented to verify the theoretical analysis. KW - Fractional cable equation KW - regularity KW - local discontinuous Galerkin method KW - stability KW - convergence DO - 10.32604/cmes.2020.08776