| 解常微分方程的稳定的显式单步法 |
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| 引用本文： | 龙爱芳,胡军浩.解常微分方程的稳定的显式单步法[J].河北科技大学学报,2013,34(1):15-17. |
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| 作者姓名： | 龙爱芳 胡军浩 |
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| 作者单位： | 中南民族大学数学与统计学学院 |
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| 基金项目： | 国家自然科学基金资助项目(60904005);湖北省自然科学基金资助项目(2009CDB026) |
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| 摘 要： | 应用函数P(x)=1A+Bx+C来近似初值问题dydx=f(x,y),y(x0)=y烅烄烆0的解,应用积分,得到了一个0烆0求解微分方程的一个新方法,它是求解常微分方程的一个显式方法,是一个单步法,最重要的是它dydx=λy,y(0)=y0,(λ<0)是稳定的,数值试验表明该方法简单有效。
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| 关 键 词： | 常微分方程 稳定 数值试验 |
| 收稿时间： | 2012/11/28 0:00:00 |
A stable explicit one-step method for solving ordinary differential equation |
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| LONG Aifang and HU Junhao.A stable explicit one-step method for solving ordinary differential equation[J].Journal of Hebei University of Science and Technology,2013,34(1):15-17. |
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| Authors: | LONG Aifang and HU Junhao |
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| Institution: | (School of Mathematics and Statistics,South-central University for Nationalities,Wuhan Hubei 430074,China) |
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| Abstract: | In this paper,function P(x)=1A+Bx+C is the approximation solution of the ordinary differential equation dydx=f(x,y),y(x0)=y0. With the integral applied,a new numerical method of ordinary differential equation is proposed.It is a stable explicit one-step method for soving ordinary differential equation.The most impotant thing is that it is stable when the method is applied to the test eqution dydx=λy, y(0)=y0(λ<0).The numerical experiments show that the method is effective. |
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| Keywords: | ordinary differential equation stable numerical experiment |
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