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.