@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} }