动态系统刚性延迟微分方程的稳定性分析  

Stability of Stiff Delay Differential Equation

作　　者：季隽[1] 王菲[1] 

机构地区：[1]大连轻工业学院数理教学部,辽宁大连116034

出　　处：《大连轻工业学院学报》1999年第1期85-90,共6页Journal of Dalian Institute of Light Industry

摘　　要：动态系统剧性延迟微分方程广泛应用于工程科学中。本文主要分析其改进问题和线性隐式Runge－Kutta插值法对刚性延迟微分方程的稳定性。提出改进问题和线性隐式单步插值法稳定性的充分条件。这些条件允许计算稳定域的边界轨迹。指出用恰当的稳定函数任意改进问题和任意线性隐式Runge－Kutta－Lagrange法是p（β）－稳定的，且线性隐式Runge－Kutta－Lagrange法比线性隐式Runge－Kutta－Hermite法具有更好的稳定性。Stiff delay differential equation is generally encountered in engineering dynamic systems. This paper discusses its modified problem and the stability of Runge-Kutta linear implicitinterpolation in solving this problem is investigated. The full condition about the stability of linearimplicit single-step inteoplation and its modification are proposed. This condition permits tocaculate the boundary locus of the stable range. It is proved that an arbitrary modified problemwith a suitable stable function and an arbitrny Runge-Kutta-Lagrange linear implicit methodarep (β)-stable. It is verified also that this Runge-Kutta-Lagrange method is more stable thanRunge-Kutta-Hermite linear implicit interpolation.

关 键 词：动态系统 微分方程 稳定性 刚性延迟 

分 类 号：TB11[理学—数学]