| 双曲型方程的Crank-Nicolson块中心差分方法 |
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| 引用本文： | 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(北京),2011,29(9). |
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| 作者姓名： | 任宗修 张秀春 银召利 |
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| 作者单位： | 河南师范大学数学与信息科学学院,河南新乡,453007 |
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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.
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| 关 键 词： | 双曲型微分方程 Crank-Nicolson块中心差分方法 误差估计 |
Crank-Nicolson Block-centered Finite Differences Method for Hyperbolic Problems |
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| REN Zongxiu,ZHANG Xiuchun,YIN Zhaoli.Crank-Nicolson Block-centered Finite Differences Method for Hyperbolic Problems[J].Science & Technology Review,2011,29(9). |
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| Authors: | REN Zongxiu ZHANG Xiuchun YIN Zhaoli |
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| Institution: | REN Zongxiu,ZHANG Xiuchun,YIN Zhaoli College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,Henan Province,China |
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| 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 ... |
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| Keywords: | hyperbolic differential equation Crank-Nicolson block-centered finite differences method error estimation |
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