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 - <p style="text-align: justify;">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.</p>