[1]范振成.常微分方程波形松弛方法的收敛稳定[J].福建工程学院学报,2021,19(06):556-559.[doi:10.3969/j.issn.1672-4348.2021.06.009]
　FAN Zhencheng.Convergent stability of waveform relaxation methods for ordinary differential equations[J].Journal of FuJian University of Technology,2021,19(06):556-559.[doi:10.3969/j.issn.1672-4348.2021.06.009]
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常微分方程波形松弛方法的收敛稳定()
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《福建工程学院学报》[ISSN:2097-3853/CN:35-1351/Z]

卷:
第19卷
期数:
2021年06期
页码:
556-559
栏目:
出版日期:
2021-12-25

文章信息/Info

Title:
Convergent stability of waveform relaxation methods for ordinary differential equations
作者:
范振成
闽江学院
Author(s):
FAN Zhencheng
School of Mathematics and Data Science, Minjiang University
关键词:
常微分方程; 波形松弛方法; Lipschitz条件; 收敛稳定
Keywords:
ordinary differential equation;  waveform relaxation method;  Lipschitz condition;  convergent stability
分类号:
O241.81
DOI:
10.3969/j.issn.1672-4348.2021.06.009
文献标志码:
A
摘要:
波形松弛方法是一种用于近似求解常微分方程的迭代方法，实际计算时，初始值和每次迭代计算不可避免存在误差， 因此有必要研究误差的传播规律， 即稳定性。对常微分方程， 证明了在Lipschitz 条件下WR 方法是收敛稳定的，即在标准收敛条件下，只要初值和历次迭代的误差足够小，由WR 方法所得近似解的扰动能被控制在给定范围内。
Abstract:
The waveform relaxation (WR) method is an iterative method for the approximate solution of ordinary differential equations (ODEs). In actual calculation, the initial value and iterative calculation inevitably have errors. Thus, it is necessary to study the propagation law of errors, i.e., the stability. The convergent stability of WR methods for ODEs is proved under the Lipschitz condition. That is, under standard convergence conditions, the perturbation of approximate solutions obtained by WR methods can be controlled within a given range as long as the error between the initial value and the previous iteration is small enough.

参考文献/References:

[1] LELARASMEE E, RUEHLI A E, SANGIOVANNI-VINCENTELLI A L. The waveform relaxation method for time-domain analysis of large scale integrated circuits[J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1982, 1（3）: 131-145.[2] BELLEN A, JACKIEWICZ Z, ZENNARO M. Contractivity of waveform relaxation runge-kutta iterations and related limit methods for dissipative systems in the maximum norm[J]. SIAM Journal on Numerical Analysis, 1994, 31（2）: 499-523.[3] 范振成. 波形松弛方法的绝对稳定与压缩[J]. 数值计算与计算机应用, 2019, 40（3）: 230-242.[4] 范振成. 泛函微分方程波形松弛方法的收敛稳定[J]. 高校应用数学学报(A辑), 2020, 35（1）: 73-82.[5] BARTOSZEWSKI Z, KWAPISZ M. On error estimates for waveform relaxation methods for delay-differential equations[J]. SIAM Journal on Numerical Analysis, 2000, 38（2）: 639-659.

更新日期/Last Update: 2021-12-25