非线性微分代数方程的一种离散波形松弛算法  

Discrete Waveform Relaxation Method of Nonlinear Differential-Algebraic Equations

作　　者：黄乘明[1] 王海霞[1] 

机构地区：[1]华中科技大学数学系,武汉430074

出　　处：《系统仿真学报》2007年第5期1000-1002,共3页Journal of System Simulation

基　　金：国家自然科学基金(10671078);教育部新世纪优秀人才支持计划(NCET-05-0638);留学回国人员科研启动基金

摘　　要：讨论用迭代方法求解微分代数方程。针对一类非线性微分代数方程连续时间波形松弛迭代格式,应用一般的单支方法和线性多步法,得到离散时间波形松弛迭代格式。在假定分裂函数满足Lipschitz条件的前提下,通过矩阵正则分裂和特殊矩阵相关性质的运用,获得离散波形松弛迭代的收敛性条件,拓展和改进了相关文献中的一些结果。Iterative methods for differential-algebraic systems are considered. General one-leg methods and linear multistep methods are applied to the continuous-time waveform relaxation iteration schemes for a class of nonlinear differential-algebraic equations and the discrete-time waveform relaxation schemes are obtained. Under the assumption that the splitting function satisfies a Lipschitz condition, some convergence conditions of the discrete waveform relaxation schemes are given. A few existing results are extended and improved. The proof is based on the properties of regular splitting of matrices and special matrices.

关 键 词：非线性微分代数方程 波形松弛 单支方法 线性多步法 

分 类 号：O241.8[理学—计算数学]