Stability and Convergence of $L1$-Galerkin Spectral Methods for the Nonlinear Time Fractional Cable Equation
Year: 2023
Author: Yanping Chen, Xiuxiu Lin, Mengjuan Zhang, Yunqing Huang
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 22–46
Abstract
A numerical scheme for the nonlinear fractional-order Cable equation with Riemann-Liouville fractional derivatives is constructed. Using finite difference discretizations in the time direction, we obtain a semi-discrete scheme. Applying spectral Galerkin discretizations in space direction to the equations of the semi-discrete systems, we construct a fully discrete method. The stability and errors of the methods are studied. Two numerical examples verify the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.020521.140522
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 1 : pp. 22–46
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Nonlinear fractional cable equation spectral method stability error estimate.
Author Details
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