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On Caputo-Type Cable Equation: Analysis and Computation

Zhen Wang1, *
1 Department of Mathematics, Shanghai University, Shanghai, 200444, China.
∗ Corresponding Author: Zhen Wang. Email: .
(This article belongs to this 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 + 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.

Keywords

Fractional cable equation, regularity, local discontinuous Galerkin method, stability, convergence.

Cite This Article

Wang, Z. (2020). On Caputo-Type Cable Equation: Analysis and Computation. CMES-Computer Modeling in Engineering & Sciences, 123(1), 353–376.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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