一类二阶延迟微分方程梯形方法的延迟依赖稳定性分析  

DELAY-DEPENDENT STABILITY ANALYSIS OF THE TRAPEZIUM RULE FOR A CLASS OF SECOND ORDER DELAY DIFFERENTIAL EQUATIONS

作　　者：黄乘明[1] 李文皓[1] 

机构地区：[1]华中科技大学数学系,武汉430074

出　　处：《计算数学》2007年第2期155-162,共8页Mathematica Numerica Sinica

基　　金：国家自然科学基金(No.10671078);教育部新世纪优秀人才支持计划;留学回国人员科研启动基金资助项目.

摘　　要：本文涉及一类二阶延迟微分方程数值方法的稳定性研究．通过运用边界轨迹法,分析了梯形方法的延迟依赖稳定区域并找到其准确边界．随后建立了解析和数值稳定区域的联系并从理论上证明了梯形方法能完全保持模型问题的延迟依赖稳定性．This paper is concerned with the study of the stability of numerical methods for a class of second order delay differential equations. By using the boundary locus method, the delay-dependent stability region of the trapezium rule is analyzed and its boundary is found. Then the relationship between analytical and numerical stability regions is identified and it is proved theoretically that the trapezium rule can completely preserve the delay-dependent stability for the considered set of test problems.

关 键 词：梯形方法 延迟依赖稳定区域 二阶延迟微分方程 

分 类 号：O241.8[理学—计算数学]