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

共 50 条

[41] Spectral iterative method and convergence analysis for solving nonlinear fractional differential equation
Yarmohammadi, M.
Javadi, S.
Babolian, E.
JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 359 : 436 - 450
[42] Spectral-Galerkin methods for the fully nonlinear Monge-Ampere equation
Jin, Lixiang
Li, Zhaoxiang
Wang, Peipei
Yi, Lijun
APPLIED NUMERICAL MATHEMATICS, 2025, 207 : 621 - 641
[43] Backward difference formulae and spectral Galerkin methods for the Riesz space fractional diffusion equation
Xu, Yang
Zhang, Yanming
Zhao, Jingjun
MATHEMATICS AND COMPUTERS IN SIMULATION, 2019, 166 : 494 - 507
[44] Error Estimates of Spectral Galerkin Methods for a Linear Fractional Reaction-Diffusion Equation
Zhang, Zhongqiang
JOURNAL OF SCIENTIFIC COMPUTING, 2019, 78 (02) : 1087 - 1110
[45] A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Diffusion Equation
Sheng, Changtao
Shen, Jie
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2018, 11 (04) : 854 - 876
[46] An L1 Legendre-Galerkin spectral method with fast algorithm for the two-dimensional nonlinear coupled time fractional Schrodinger equation and its parameter estimation
Jia, Junqing
Jiang, Xiaoyun
Zhang, Hui
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 82 : 13 - 35
[47] Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain
Wang, Pengde
APPLIED MATHEMATICS LETTERS, 2021, 112
[48] Muntz Spectral Methods for the Time-Fractional Diffusion Equation
Hou, Dianming
Hasan, Mohammad Tanzil
Xu, Chuanju
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2018, 18 (01) : 43 - 62
[49] Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space fractional diffusion equation
Zhao, Jingjun
Zhang, Yanming
Xu, Yang
APPLIED MATHEMATICS AND COMPUTATION, 2020, 386
[50] Efficient Galerkin finite element methods for a time-fractional Cattaneo equation
Chen, An
Nong, Lijuan
ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)

← 1 2 3 4 5 →