Unconditionally convergent numerical method for the two-dimensional nonlinear time fractional diffusion-wave equation

被引：20

作者：

Zhang, Hui ^{[1
]}

Jiang, Xiaoyun ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2019年 / 146卷

基金：

中国国家自然科学基金;

关键词：

Two-dimensional nonlinear time fractional diffusion-wave equation; Optimal error estimate; Crank-Nicolson method; Legendre spectral method; ADVECTION-DISPERSION EQUATIONS; SPECTRAL METHOD; SINE-GORDON; ANOMALOUS DIFFUSION; GALERKIN METHOD; ELEMENT-METHOD; APPROXIMATIONS;

D O I：

10.1016/j.apnum.2019.06.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop a Crank-Nicolson Legendre spectral method for solving the two-dimensional nonlinear time fractional diffusion-wave equation in bounded rectangular domains. In terms of the error splitting argument technique, an optimal error estimate of the numerical scheme is obtained without any time-step size conditions, while the usual analysis for high dimensional nonlinear fractional problems always required certain time-step restrictions dependent on the spatial mesh size. Some numerical results are given to justify the theoretical analysis. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：1 / 12

页数：12

共 50 条

[1] A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations
Huang, Jianfei
Zhang, Jingna
Arshad, Sadia
Tang, Yifa
[J]. APPLIED NUMERICAL MATHEMATICS, 2021, 159 : 159 - 173
[2] Analysis and numerical approximation of the fractional-order two-dimensional diffusion-wave equation
Rafaqat, Kanza
Naeem, Muhammad
Akgul, Ali
Hassan, Ahmed M.
Abdullah, Farah Aini
Ali, Umair
[J]. FRONTIERS IN PHYSICS, 2023, 11
[3] The analytical solution and numerical solutions for a two-dimensional multi-term time fractional diffusion and diffusion-wave equation
Shen, Shujun
Liu, Fawang
Anh, Vo V.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 345 : 515 - 534
[4] The Galerkin spectral element method for the solution of two-dimensional multiterm time fractional diffusion-wave equation
Saffarian, Marziyeh
Mohebbi, Akbar
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (04) : 2842 - 2858
[5] A meshless method for time fractional nonlinear mixed diffusion and diffusion-wave equation
Bhardwaj, Akanksha
Kumar, Alpesh
[J]. APPLIED NUMERICAL MATHEMATICS, 2021, 160 : 146 - 165
[6] TWO-DIMENSIONAL FRACTIONAL EULER POLYNOMIALS METHOD FOR FRACTIONAL DIFFUSION-WAVE EQUATIONS
Balachandar, S. Raja
Venkatesh, S. G.
Balasubramanian, K.
Uma, D.
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2023, 31 (04)
[7] A high-order numerical algorithm for two-dimensional time-space tempered fractional diffusion-wave equation
Ding, Hengfei
[J]. APPLIED NUMERICAL MATHEMATICS, 2019, 135 : 30 - 46
[8] Error analysis of direct discontinuous Galerkin method for two-dimensional fractional diffusion-wave equation
An, Na
Huang, Chaobao
Yu, Xijun
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 349 : 148 - 157
[9] A high-order ADI scheme for the two-dimensional time fractional diffusion-wave equation
Wang, Zhibo
Vong, Seakweng
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2015, 92 (05) : 970 - 979
[10] An RBF Based Finite Difference Method for the Numerical Approximation of Multi-term Nonlinear Time Fractional Two Dimensional Diffusion-Wave Equation
Bhardwaj A.
Kumar A.
Tiwari A.K.
[J]. International Journal of Applied and Computational Mathematics, 2022, 8 (2)

← 1 2 3 4 5 →