| 非线性常微分方程边值问题的数值近似 |
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| 引用本文： | 陈誌敏.非线性常微分方程边值问题的数值近似[J].武汉工程职业技术学院学报,2007,19(2):77-80. |
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| 作者姓名： | 陈誌敏 |
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| 作者单位： | 武汉工交职业学院,武汉,430205 |
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| 摘 要： | 迭代亏量校正法常用于非线性常微分方程边值问题的数值求解，该方法可达到的最高精度受限于精确解的光滑性以及插值多项式的次数。本文通过对原迭代方法计算格式的改造，使改进的迭代亏量校正法的收敛阶显著提高。此外还讨论了该方法的收敛问题。数值实验结果表明，所给出的计算方法是十分有效的。
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| 关 键 词： | 边值问题 迭代校正 收敛阶 |
| 文章编号： | 1671-3524（2007）02-0077-04 |
| 修稿时间： | 2007-03-12 |
Numerical Approximation to Nonlinear BVPs in ODEs |
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| CHEN Zhimin.Numerical Approximation to Nonlinear BVPs in ODEs[J].Journal of University for Staff and Workers of Wuhan Iron and Steel(Group)Corporation,2007,19(2):77-80. |
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| Authors: | CHEN Zhimin |
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| Institution: | CHEN Zhimin |
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| Abstract: | This paper discusses the improvement on Iterated Defect Correction for boundary value problems in nonlinear ordinary differential equations. The maximal attainable accuracy of the original iterated method was limited by the smoothness of the exact solution and order of polynomial interpolation. The modified format of the original algorithm improves maximal achievable convergence order, and the numerical experiments indicate that the given method is more effective. |
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| Keywords: | boundary value problems iterated correction convergence order |
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