| 非线性高阶微分方程初值问题的波形松弛方法 |
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| 引用本文： | 马菊侠,吴云天,白云霄.非线性高阶微分方程初值问题的波形松弛方法[J].哈尔滨工业大学学报,2004,36(8):1077-1079. |
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| 作者姓名： | 马菊侠 吴云天 白云霄 |
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| 作者单位： | 陕西科技大学,理学院,陕西,咸阳,712081;陕西科技大学,计算机与信息工程学院,陕西,咸阳,712081 |
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| 基金项目： | 陕西科技大学科研基金资助项目(zx-29). |
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| 摘 要： | 用范数估计方法对非线性高阶微分方程的初值问题进行了讨论，给出了系统函数对某些变量偏导数的某种范数小于1时，非线性高阶微分方程的波形松弛算法产生的迭代序列收敛到该方程初值解的充分性条件．该充分性条件实用性很强，对高阶方程容易判定其波形松弛序列的收敛性．
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| 关 键 词： | 非线性高阶微分方程 波形松弛 初值问题 |
| 文章编号： | 0367-6234(2004)08-1077-03 |
| 修稿时间： | 2002年3月29日 |
Waveform relaxation of initial problem of nonlinear high-order differential equations |
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| MA Ju-xia,WU Yun-tian,BAI Yun-xiao.Waveform relaxation of initial problem of nonlinear high-order differential equations[J].Journal of Harbin Institute of Technology,2004,36(8):1077-1079. |
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| Authors: | MA Ju-xia WU Yun-tian BAI Yun-xiao |
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| Affiliation: | MA Ju-xia~1,WU Yun-tian~2,BAI Yun-xiao~1 |
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| Abstract: | Norm method is used to discuss the periodic boundary problems of high-order nonlinear differential equations. A theorm is presented to safeguard the convergence of waveform relaxation (WR) solutions of a dynamic system described by implicit nonlinear ordinary differential equations (ODEs) with an initial constraint. If the norm of functions issued from the system is less than one, the proposed WR algorithm is convergent to the exact solution. |
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| Keywords: | nonlinear high-order differential equations waveform relaxation initial problem |
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