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

被引：3

作者：

Chen, Yanping ^{[1
]}

Lin, Xiuxiu ^{[1
]}

Zhang, Mengjuan ^{[2
]}

Huang, Yunqing ^{[2
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2023年 / 13卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Nonlinear fractional cable equation; spectral method; stability; error estimate; FINITE DIFFERENCE/SPECTRAL APPROXIMATIONS; COLLOCATION METHOD; DIFFUSION; SCHEME;

D O I：

10.4208/eajam.020521.140522

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：22 / 46

页数：25

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