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非线性高阶微分方程初值问题的波形松弛方法 被引量：1

Waveform relaxation of initial problem of nonlinear high-order differential equations
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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. Norm method is used to discuss the periodic boundary problems of high-order nonlinear differential equations. A theorem 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.
作者 马菊侠 吴云天 白云霄
机构地区 陕西科技大学理学院 陕西科技大学计算机与信息工程学院
出处 《哈尔滨工业大学学报》 EI CAS CSCD 北大核心 2004年第8期1077-1079,共3页 Journal of Harbin Institute of Technology
基金 陕西科技大学科研基金资助项目(zx-29).
关键词 非线性高阶微分方程 初值问题 波形松弛方法 微分中值定理 Convergence of numerical methods Ordinary differential equations Relaxation processes Waveform analysis
分类号 O175.1 [理学—基础数学]
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参考文献8

  • 1[1]CHUA L O, DESOER C A, KUH E S. Linear and Nonlinear Circuits [ M ]. New York: McGraw - Hill, 1987.
  • 2[2]HSU C S. Cell-to-Cell Mapping--A Method of Global Analysis for Nonlinear Systems [ M ]. New York: SpringVerlag, 1986.
  • 3[3]LALARSMEE E, RUEHLI A, SANGIOVANNI-VINCENTELLI A L. The waveform relaxation method for time-domain analysis of large scale integrated circuits[J]. IEEE Trans CAD of IC and Sys, 1982,1 (30):131 - 145.
  • 4[4]JIANG Y L, WING O. Monotone waveform relaxation for systems of nonlinear differential-algebraic equations[J]. SIAM J Numer Anal, 2000,38 ( 1 ): 170 - 185.
  • 5[5]JIANG Y L. Periodic waveform relaxation solutions of nonlinear dynamic equations [ J ]. App Math and Comp,2003,135:219 - 226.
  • 6[6]JIANG Y L, CHEN R M M, WING O. Periodic waveform relaxation of nonlinear dynamic equations by QuasiLinearization[J]. IEEE Trans Circuits Syst I, 2003,50(40) :589-593.
  • 7[7]JANKOWSKI T. Waveform relaxation method for periodic differential-functional systems [ J ]. J Computational and App Math ,2003,156:457 - 469.
  • 8[8]JIANG Y L, CHEN R M M,WING O. Waveform relaxation of nonlinear second-order differential equations [ J ].IEEE Trans Circuits Syst I, 2001,48 ( 11 ): 1344 -1347.

同被引文献9

  • 1CHUA L O, DESOE C A, KUH E S. Linear and Nonlinear Circuits [ M ]. New York : McGraw-Hill, 1987.
  • 2HSU C S. Cell-to-Cell Mapping——A Method of Global Analysis for Nonlinear Systems [ M ]. New York: Spring- Verlag, 1986.
  • 3LALARASMEE E, RUEHLI A, SANGIOVANNI-VINCENTELLI A L. The waveform relaxation method for time-domain analysis of large scale integrated circuits [ J ]. IEEE Trans CAD of IC and Sys, 1982,1(3) :131 -145.
  • 4HUANG Z L, JIANG Y L, CHEN R M M, et al. Parallel implementation of dynamic equations for solving eigenvalue problems of complex matrix [ C]//Proc 4^th Int Conf Algorithms and Architectures for Parallel Processing. Hong Kong : [ s. n. ], 2000.
  • 5JIANG Y; L. WING O. Monotone waveform relaxation for systems of nonlinear differential-algebraic equations [J]. SIAM J Numer Anal, 2000,38(1):170 -185.
  • 6JIANG Y L. Periodic waveform relaxation solutions of nonlinear dynamic equations [ J]. App Math and Comp, 2003,135:219 -226.
  • 7JIANG Y L, CHEN R M M, WING O. A waveform relaxation approach to determining periodic responses of nonlinear differential-algebraic equations [ C ]// Proceedings of the 2001 IEEE International Symposium on Circuits and Systems. Sydney: [ s. n. ], 2001:443 - 446.
  • 8JANKOWSKI T. Waveform relaxation method for periodic differential-functional systems [ J ]. J Computational and App Math, 2003,156(2) :457-469.
  • 9蔺小林,王玉萍,王晓琴.非线性微分系统的动力迭代方法[J].哈尔滨工业大学学报,2009,41(1):235-238. 被引量：1

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哈尔滨工业大学学报
2004年 第8期

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