[1]范振成.指数波形松弛方法[J].福建工程学院学报,2017,15(04):364-366.[doi:10.3969/j.issn.1672-4348.2017.04.011]
　Fan Zhencheng.Exponential waveform relaxation methods[J].Journal of FuJian University of Technology,2017,15(04):364-366.[doi:10.3969/j.issn.1672-4348.2017.04.011]
点击复制

指数波形松弛方法()
分享到：

《福建工程学院学报》[ISSN:2097-3853/CN:35-1351/Z]

卷:
第15卷
期数:
2017年04期
页码:
364-366
栏目:
出版日期:
2017-08-25

文章信息/Info

Title:
Exponential waveform relaxation methods
作者:
范振成
闽江学院数学系
Author(s):
Fan Zhencheng
Mathematics Department, Minjiang University
关键词:
刚性微分方程;  指数方法;  波形松弛方法
Keywords:
stiff differential equation;  exponential method;  waveform relaxation method
分类号:
O241.81
DOI:
10.3969/j.issn.1672-4348.2017.04.011
文献标志码:
A
摘要:
结合常微分方程的指数方法和波形松弛方法, 建立指数波形松弛方法。然后证明了该方法是收敛的。最后通过算例与显式欧拉方法、指数方法和波形松弛方法进行对比。结果表明，对于弱耦合的大系统, 指数波形松弛方法具有一定优势。
Abstract:
Firstly, the exponential waveform relaxation methods (EWRMs) for ordinary differential equations are established by combining the exponential methods (EMs) and the waveform relaxation methods (WRMs). Secondly, the convergence of the EWRMs is confirmed. Lastly, numerical experimentation is conducted to make a comparison among the explicit Euler methods, EMs and WRMs. The results indicate that the EWRMs are advantageous for large weakly coupled systems of ordinary differential equations.

参考文献/References:

[1] 袁兆鼎,费景高,刘德贵.刚性常微分方程初值问题的数值解法[M].北京：科学出版社,1987.
[2] Dekker K,Verwer J G. Stability of RungeKutta methods for stiff nonlinear differential equatons[M].Amsterdam:Elsevier Science Ltd,1984.
[3] Hochbruck M,Ostermann A. Exponential multistep methods of Adamstype[J]. Numerical Mathematics,2011,51(4):889-908.
[4] Xu Y, Zhao J J, Sui Z N. Exponential RungeKutta methods for delay differential equations[J]. Mathematics and Computers in Simulation,2010,80(12):2350-2361.
[5] Hout K J.On the convergence of waveform relaxation methods for stiff nonlinear ordinary differential equations[J].Applied Numerical Mathematics,1995,18(1):175-190.
[6] Zhou S, Huang T Z. Convergence of waveform relaxation methods for Hermitian positive definite linear systems[J]. Applied Mathematics and Computation,2008,203(2):943-952.
[7] 张平文,李铁军.数值分析[M].北京:北京大学出版社, 2007.

更新日期/Last Update: 2017-08-25