@Article{cmes.2020.08776,
AUTHOR = {Zhen Wang},
TITLE = {On Caputo-Type Cable Equation: Analysis and Computation},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {123},
YEAR = {2020},
NUMBER = {1},
PAGES = {353--376},
URL = {http://www.techscience.com/CMES/v123n1/38497},
ISSN = {1526-1506},
ABSTRACT = {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.},
DOI = {10.32604/cmes.2020.08776}
}