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

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