Stability and Convergence of $L1$-Galerkin Spectral Methods for the Nonlinear Time Fractional Cable Equation

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

Yanping Chen

Xiuxiu Lin

Mengjuan Zhang

Yunqing Huang

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