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