| 解非线性常微分方程边值问题差分方程的数值延拓法 |
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| 引用本文： | 钮群.解非线性常微分方程边值问题差分方程的数值延拓法[J].河海大学学报(自然科学版),2006,34(3):345-348. |
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| 作者姓名： | 钮群 |
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| 作者单位： | 河海大学理学院,江苏,南京,210098 |
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| 摘 要： | 非线性常微分方程的差分方程是一个非线性方程组.根据解非线性方程组的全局收敛方法,采用数值延拓法研究常微分方程边值问题数值解的计算方法,并给出了该算法为全局收敛的充分条件.通过计算具体算例的数值解,表明该计算方法是可行的.
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| 关 键 词： | 边值问题 差分方程 同胚 全局收敛 数值延拓法 |
| 文章编号： | 1000-1980（2006）03-0345-04 |
| 收稿时间： | 2004-09-28 |
| 修稿时间： | 2004-09-28 |
Numerical continuation method for solving nonlinear difference equations of ordinary differential equation boundary value problem |
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| NIU Qun.Numerical continuation method for solving nonlinear difference equations of ordinary differential equation boundary value problem[J].Journal of Hohai University (Natural Sciences ),2006,34(3):345-348. |
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| Authors: | NIU Qun |
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| Institution: | College of Sciences, Hohai University, Nanjing 210098, China |
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| Abstract: | For obtaining the numerical solution to the nonlinear difference equations of ordinary differential equation boundary value problem,it is necessary to solve a system of nonlinear equations.Based on the global convergence method for solving the nonlinear equations,the numerical continuation method was adopted to find the numerical solution to nonlinear difference equations of ordinary differential equation boundary value problem,and the sufficient condition was given for the numerical method to realize the global convergence.An example was given to demonstrate the feasibility of the numerical method. |
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| Keywords: | boundary value problem difference equation homeomorphism global convergence numerical continuation method |
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