| 二阶常微分方程初值问题的Laguerre-Gauss配置法 |
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| 引用本文： | 严建平,郭本瑜.二阶常微分方程初值问题的Laguerre-Gauss配置法[J].应用数学和力学,2011,32(12):1439-1460. |
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| 作者姓名： | 严建平 郭本瑜 |
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| 作者单位： | 上海师范大学 数学系,上海 200234; |
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| 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) |
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| 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．
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| 关 键 词： | Laguerre-Gauss配置方法 二阶常微分方程 初值问题 |
| 收稿时间： | 2011-08-17 |
Laguerre-Gauss Collocation Method for Initial Values Problems of Second Order ODEs |
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| YAN Jian-ping
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GUO Ben-yu.Laguerre-Gauss Collocation Method for Initial Values Problems of Second Order ODEs[J].Applied Mathematics and Mechanics,2011,32(12):1439-1460. |
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| Authors: | YAN Jian-ping GUO Ben-yu |
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| Institution: | 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 |
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| 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 Laguerre-Gauss interpolation.A multi-step collocation method was also provided,which simplified actual computation and still... |
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| Keywords: | Laguerre-Gauss collocation method initial value problems second order ODEs |
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