Zhen Wang1, *
CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.1, pp. 353-376, 2020, DOI:10.32604/cmes.2020.08776
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. More >
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