Volume 13, Issue 1
Stability and Convergence of $L1$-Galerkin Spectral Methods for the Nonlinear Time Fractional Cable Equation

East Asian J. Appl. Math., 13 (2023), pp. 22-46.

Published online: 2023-01

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• 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.

35R11, 65M12, 65M70

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@Article{EAJAM-13-22, author = {Chen , YanpingLin , XiuxiuZhang , Mengjuan and Huang , Yunqing}, title = {Stability and Convergence of $L1$-Galerkin Spectral Methods for the Nonlinear Time Fractional Cable Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.020521.140522}, url = {http://global-sci.org/intro/article_detail/eajam/21300.html} }
TY - JOUR T1 - Stability and Convergence of $L1$-Galerkin Spectral Methods for the Nonlinear Time Fractional Cable Equation AU - Chen , Yanping AU - Lin , Xiuxiu AU - Zhang , Mengjuan AU - Huang , Yunqing JO - East Asian Journal on Applied Mathematics VL - 1 SP - 22 EP - 46 PY - 2023 DA - 2023/01 SN - 13 DO - http://doi.org/10.4208/eajam.020521.140522 UR - https://global-sci.org/intro/article_detail/eajam/21300.html KW - Nonlinear fractional cable equation, spectral method, stability, error estimate. AB -

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.

Yanping Chen, Xiuxiu Lin, Mengjuan Zhang & Yunqing Huang. (2023). Stability and Convergence of $L1$-Galerkin Spectral Methods for the Nonlinear Time Fractional Cable Equation. East Asian Journal on Applied Mathematics. 13 (1). 22-46. doi:10.4208/eajam.020521.140522
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