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.
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页码：1 / 12
页数：12
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