A Crank-Nicolson collocation spectral method for the two-dimensional telegraph equations.

IF 1.6 3区数学 Q1 Mathematics

Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-19 DOI:10.1186/s13660-018-1728-5

Yanjie Zhou, Zhendong Luo

引用次数: 9

Abstract

In this paper, we mainly focus to study the Crank-Nicolson collocation spectral method for two-dimensional (2D) telegraph equations. For this purpose, we first establish a Crank-Nicolson collocation spectral model based on the Chebyshev polynomials for the 2D telegraph equations. We then discuss the existence, uniqueness, stability, and convergence of the Crank-Nicolson collocation spectral numerical solutions. Finally, we use two sets of numerical examples to verify the validity of theoretical analysis. This implies that the Crank-Nicolson collocation spectral model is very effective for solving the 2D telegraph equations.

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二维电报方程的Crank-Nicolson搭配谱法。

本文主要研究二维(2D)电报方程的Crank-Nicolson搭配谱方法。为此，我们首先对二维电报方程建立了基于Chebyshev多项式的Crank-Nicolson搭配谱模型。然后讨论了Crank-Nicolson配置谱数值解的存在性、唯一性、稳定性和收敛性。最后，用两组数值算例验证了理论分析的有效性。这意味着Crank-Nicolson搭配谱模型对于求解二维电报方程是非常有效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.