| 一种求解常微分方程初值问题的单步法 |
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| 引用本文： | 靳绍礼.一种求解常微分方程初值问题的单步法[J].科学技术与工程,2010,10(31). |
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| 作者姓名： | 靳绍礼 |
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| 作者单位： | 济南大学理学院,济南,250022 |
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| 基金项目： | 博士基金（XBS0929） |
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| 摘 要： | 本文利用Cotes求积公式推出求解常微分方程初值问题的5点6阶方法，进而用Newton-Cotes求积公式，推出了求解常微分方程初值问题的更为一般的公式，并给出了相应方法的绝对稳定区间，最后通过数值算例表明，该方法具有一定的优势。
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| 关 键 词： | 一阶常微分方程 单步方法 Cotes求积公式 绝对稳定 相容阶 |
| 收稿时间： | 2010/8/19 0:00:00 |
| 修稿时间： | 8/27/2010 9:49:44 AM |
A Class of Step Method for Solving Initial Value Problems of Ordinary Differential Equations |
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| jinshaoli.A Class of Step Method for Solving Initial Value Problems of Ordinary Differential Equations[J].Science Technology and Engineering,2010,10(31). |
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| Authors: | jinshaoli |
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| Institution: | JIN Shao-li,LI Ti-yun,SONG Yu-cheng(School of Science,University of Jinan,Jinan 250022,P.R.China) |
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| Abstract: | With Cotes-integration,a class of one step method is got for solving initial value of ordinary differential equations,which is 5 point 6 order method,then with Newton-Cotes-integration.A general method for solving initial value of orinary differential equations is got.At the same time,the corresponding mentods'absolute stability is got.Numerical tests show that these methods are efficient. |
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| Keywords: | orinary differential equations one step method Cotes-integration absolute stability consistency-order |
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