| 一阶微分方程解的存在性的再讨论 |
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| 引用本文： | 王锐利,林大志. 一阶微分方程解的存在性的再讨论[J]. 济源职业技术学院学报, 2010, 9(2): 13-16. DOI: 10.3969/j.issn.1672-0342.2010.02.005 |
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| 作者姓名： | 王锐利 林大志 |
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| 作者单位： | 济源职业技术学院,河南,济源,459000;郑州牧业工程高等专科学校,河南,郑州,450011 |
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| 摘 要： | 把欧拉折线法与改进的欧拉数值解法结合起来,对佩亚诺存在定理进行了新的证明。当未知函数可进行适当的泰勒展开（若未知函数2阶,甚至3阶可导）时,无论在证明上,还是在进行简单的数值计算方面都有一定的意义,这样就有可能提高数值计算时的精度以及要求精确解的步数减少。
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| 关 键 词： | 佩亚诺存在定理 欧拉折线法 改进的欧拉数值解法 线素 |
Existence of Solution on First Order Ordinary Differential Equation |
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| WANG Rui-li,LIN Da-zhi. Existence of Solution on First Order Ordinary Differential Equation[J]. JOurnal of Jiyuan Vocational and Technical College, 2010, 9(2): 13-16. DOI: 10.3969/j.issn.1672-0342.2010.02.005 |
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| Authors: | WANG Rui-li LIN Da-zhi |
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| Affiliation: | 1.Jiyuan Vocational and Technical College,Jiyuan 459000,Henan,China;2.Zhengzhou College of Animal Husbandry Engineering,Zhengzhou 450011,Henan China) |
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| Abstract: | Combination of Euler method with modified Euler numerical method,proves Peano existence theorem.If the unknown function can have some Taylor series expansion（second or third derivative）,it is significant in proving or numerical computing.Furthermore,it not only improves the precision on the numerical computing,but also reduces the steps which satisfy the required precision. |
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| Keywords: | Peano existence theorem Euler method modified Euler numerical method line element |
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