双曲型方程的Crank-Nicolson块中心差分方法

任宗修;张秀春;银召利

doi:10.3981/j.issn.1000-7857.2011.09.009

科技导报 >

2011 , Vol. 29 >Issue 11-09: 57 - 61

DOI: https://doi.org/10.3981/j.issn.1000-7857.2011.09.009

研究论文

双曲型方程的Crank-Nicolson块中心差分方法

任宗修;张秀春;银召利

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河南师范大学数学与信息科学学院，河南新乡 453007

收稿日期: 2010-09-29

修回日期: 2011-02-09

网络出版日期: 2011-03-28

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Crank-Nicolson Block-centered Finite Differences Method for Hyperbolic Problems

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Received date: 2010-09-29

Revised date: 2011-02-09

Online published: 2011-03-28

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摘要

用Crank-Nicolson块中心差分法研究了有界区域上的线性双曲型微分方程的数值解，此方法以块中心差分方法和抛物型的Crank-Nicolson格式为基础。在非等距剖分的网格上得到了近似解和解的一阶导数。其特点是近似解按离散的L2模达到最优阶误差估计，解的一阶导数的近似解达到超收敛误差估计，达到和近似解同样的精度。本文所讨论的方法，在计算量上没有增加。数值试验结果与理论分析一致，说明格式具有高效的收敛性。

关键词： 双曲型微分方程; Crank-Nicolson块中心差分方法; 误差估计

本文引用格式

任宗修;张秀春;银召利 . 双曲型方程的Crank-Nicolson块中心差分方法[J]. 科技导报, 2011 , 29(11-09) : 57 -61 . DOI: 10.3981/j.issn.1000-7857.2011.09.009

Abstract

The Crank-Nicolson block-centered finite difference method studies the solution of the linear hyperbolic differential problems in the bounded domain with sufficiently smooth data. This method is based on both block-center finite difference method and parabolic Crank-Nicolson format. Both the approximate solution and its first derivatives are obtained for all non-uniform grids. Its characteristics are that the approximate solution according to the discrete L2-norm is achieved optimal order error estimation, and the approximate solution of the first derivatives is reached at super convergence error estimation. This method does not increase the calculation. Numerical tests are identical with theoretical analysis; it explains that the format possesses the efficient convergence.

Key words： hyperbolic differential equation; Crank-Nicolson block-centered finite differences method; error estimation

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