二阶常微分方程初值问题的Laguerre-Gauss配置法

严建平; 郭本瑜

doi:10.3879/j.issn.1000-0887.2011.12.005

二阶常微分方程初值问题的Laguerre-Gauss配置法

doi: 10.3879/j.issn.1000-0887.2011.12.005

严建平^1,2,
郭本瑜^1,3,4

上海师范大学数学系,上海 200234;
广东金融学院应用数学,广东广州 510521;
上海市高校科学计算重点实验室,上海 200234;

基金项目: 国家自然科学基金资助项目(11171227);中国教育部博士点基金资助项目(20080270001);上海市重点学科基金资助项目(S30405);上海市高校E-研究院基金资助项目(E03004);广东教育厅高校优秀青年创新人才培育资助项目(LYM09138)

详细信息

作者简介:
严建平(1975- ),男,湖南人,讲师,博士(E-mail:hnyanjianping@eyou.com);郭本瑜(1942- ),男,浙江人,教授,博士(联系人.Tel:+86-21-64322851;E-mail:byguo@shnu.edu.cn).

中图分类号: O24.81
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出版历程
- 收稿日期: 2011-08-17
- 修回日期: 2011-09-26
- 刊出日期: 2011-12-15

Laguerre-Gauss Collocation Method for Initial Values Problems of Second Order ODEs

YAN Jian-ping^1,2,
GUO Ben-yu^1,3,4

Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China;
Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, P. R. China;
Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, P. R. China;
Division of Computational Science of E-Institute of Shanghai Universities, Shanghai 200234, P. R. China

摘要

摘要: 研究二阶常微分方程初值问题的数值解法．该文中基于Laguerre-Gauss插值设计了一类新的配置法, 它易于计算，且特别适用于非线性问题．该文中分析了二种不同情况时的收敛性，并应用Laguerre-Gauss插值的最新结果，证明了它的谱精度．该文还提供了一种多步配置法，它既简化了计算，又保持同样的谱精度．数值结果显示了这些算法的高精度．
- Laguerre-Gauss配置方法 /
- 二阶常微分方程 /
- 初值问题
Abstract: Numerical method for initial value problems of second order ordinary differential equations was investigated. The new collocation method based on the Laguerre-Gauss interpolation was designed, which was very easy to be carried out, especially for nonlinear problems. The convergence was analyzed for two different cases, and the spectral accuracy was proved by using the recent results on the LaguerreGauss interpolation. A multi-step collocation method was also provided, which simplified actual computation and still kept the same spectral accuracy. The numerical results are presented, demonstrating the high accuracy of suggested algorithms.
- Laguerre-Gauss collocation method /
- initial value problems /
- second order ODEs

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参考文献(31)

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二阶常微分方程初值问题的Laguerre-Gauss配置法

doi: 10.3879/j.issn.1000-0887.2011.12.005

作者简介:
严建平(1975- ),男,湖南人,讲师,博士(E-mail:hnyanjianping@eyou.com);郭本瑜(1942- ),男,浙江人,教授,博士(联系人.Tel:+86-21-64322851;E-mail:byguo@shnu.edu.cn).

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Laguerre-Gauss Collocation Method for Initial Values Problems of Second Order ODEs

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二阶常微分方程初值问题的Laguerre-Gauss配置法

doi: 10.3879/j.issn.1000-0887.2011.12.005

作者简介: 严建平(1975- ),男,湖南人,讲师,博士(E-mail:hnyanjianping@eyou.com);郭本瑜(1942- ),男,浙江人,教授,博士(联系人.Tel:+86-21-64322851;E-mail:byguo@shnu.edu.cn).

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出版历程

Laguerre-Gauss Collocation Method for Initial Values Problems of Second Order ODEs

计量

出版历程

目录

作者简介:
严建平(1975- ),男,湖南人,讲师,博士(E-mail:hnyanjianping@eyou.com);郭本瑜(1942- ),男,浙江人,教授,博士(联系人.Tel:+86-21-64322851;E-mail:byguo@shnu.edu.cn).