Open Access

ARTICLE

On Caputo-Type Cable Equation: Analysis and Computation

Zhen Wang^{1, *}

1 Department of Mathematics, Shanghai University, Shanghai, 200444, China.

∗ Corresponding Author: Zhen Wang. Email: .

(This article belongs to the Special Issue: Numerical Methods for Differential and Integral Equations)

Computer Modeling in Engineering & Sciences 2020, 123(1), 353-376. https://doi.org/10.32604/cmes.2020.08776

Received 08 October 2019; Accepted 04 November 2019; Issue published 01 April 2020

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 + h^k+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.

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Keywords

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