求解延迟微分方程块θ-方法的GPL_m-稳定性(英文)  

GPL_m–Stability of Block θ–method for Delay Differential Equation

作　　者：丛玉豪[1] 李顺道[1] 谭秀丽[1] 

机构地区：[1]上海师范大学数学系

出　　处：《系统仿真学报》2007年第17期3937-3939,共3页Journal of System Simulation

基　　金：E-Institutes of Shanghai Municipal Education Commission (E03004);Shanghai Municipal Education Commission (04DB07, 07ZZ64);Shanghai Science and Technology Committee (03QA14036);The Special Funds for Major Specialties of Shanghai Education Committee NSFC(1067130)

摘　　要：讨论了带有多个滞时量的延时微分方程的数值稳定性,分析了用块θ–方法求解多延迟微分方程GPm–稳定和GPLm–稳定的条件,基于Lagrange插值,证明了块θ–方法GPm–稳定的充分必要条件是方法是A-稳定的,块θ–方法GPLm–稳定的充分必要条件是θ=1。The stability behavior of numerical solution for delay differential equations with many delays was studied. The conditions of GPmstability and GPLmstability of block θ-method for delay differential equations with many delays were discussed. By Lagrange Interpolation, it is shown that block θ-method is GPm-stable if and only if it is A-stable, block-θ method is GPLm-stable if and only if θ= 1.

关 键 词：延时微分方程 数值稳定性 θ-良方法 L-稳定性 

分 类 号：O241.8[理学—计算数学]