@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} }