Analysis of the L1 scheme for fractional wave equations with nonsmooth data

被引：9

作者：

Li, Binjie ^{[1
]}

Wang, Tao ^{[2
]}

Xie, Xiaoping ^{[1
]}

机构：

[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

[2] South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 90卷

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Fractional wave equation; L1; scheme; Stability; Convergence; Nonsmooth data; DISCONTINUOUS GALERKIN METHOD; EVOLUTION EQUATION; DIFFUSION; DISCRETIZATION; APPROXIMATIONS; SUPERCONVERGENCE; STABILITY; FORMULA;

D O I：

10.1016/j.camwa.2021.03.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper analyzes the well-known L1 scheme for fractional wave equations with nonsmooth data. A new stability estimate and temporal accuracy O(tau(3-alpha)) are obtained. In addition, a modified L1 scheme is proposed, and its stability and temporal accuracy O(tau(2)) are also derived under nonsmooth data. The convergence of the two schemes in the inhomogeneous case are also established. Finally, numerical experiments are performed to verify the theoretical results.

引用

页码：1 / 12

页数：12

共 50 条

[31] UNCONDITIONALLY CONVERGENT L1-GALERKIN FEMS FOR NONLINEAR TIME-FRACTIONAL SCHRODINGER EQUATIONS [J].

Li, Dongfang ;

Wang, Jilu ;

Zhang, Jiwei .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2017, 39 (06) :A3067-A3088

[32] Analysis of the L1 scheme for a time fractional parabolic-elliptic problem involving weak singularity [J].

Santra, Sudarshan ;

Mohapatra, Jugal .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (02) :1529-1541

[33] Local error analysis of L1 scheme for time-fractional diffusion equation on a star-shaped pipe network [J].

Wang, Jingjia ;

Yu, Yongguang ;

Hou, Jian ;

Meng, Xiangyun .

PHYSICA SCRIPTA, 2024, 99 (12)

[34] Pointwise-in-time error analysis of the corrected L1 scheme for a time-fractional sine-Gordon equation [J].

Huang, Chaobao ;

An, Na ;

Yu, Xijun ;

Chen, Hu .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2025, 140

[35] The decoupled Crank-Nicolson/Adams-Bashforth scheme for the Boussinesq equations with nonsmooth initial data [J].

Zhang, Tong ;

Jin, Jiaojiao ;

Jiang, Tao .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 337 :234-266

[36] Maximum bound principle preserving nonuniform L1 scheme for space-time fractional Allen-Cahn equation [J].

Jiang, Zhuhan ;

Sun, Hong ;

Zhao, Xuan .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2025,

[37] H1-norm Analysis of an Integral-Averaged L1 Method on Nonuniform Time Meshes for a Time-Fractional Diffusion Problem [J].

Zheng, Zi-Yun ;

Wang, Yuan-Ming .

JOURNAL OF SCIENTIFIC COMPUTING, 2025, 103 (03)

[38] The Crank-Nicolson/Adams-Bashforth Scheme for the Time-Dependent Navier-Stokes Equations with Nonsmooth Initial Data [J].

He, Yinnian .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2012, 28 (01) :155-187

[39] Approximate Solution of a Kind of Time-Fractional Evolution Equations Based on Fast L1 Formula and Barycentric Lagrange Interpolation [J].

Liu, Ting ;

Liu, Hongyan ;

Ma, Yanying .

FRACTAL AND FRACTIONAL, 2024, 8 (11)

[40] A unified numerical scheme for the multi-term time fractional diffusion and diffusion-wave equations with variable coefficients [J].

Chen, Hu ;

Lu, Shujuan ;

Chen, Wenping .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 330 :380-397

← 1 2 3 4 5 →