DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG  

作　　者：Hong-jiong Tian (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China) 

出　　处：《Journal of Computational Mathematics》2003年第6期715-726,共12页计算数学（英文）

基　　金：This project is supported by NSF of China (No.10101012);Shanghai Rising Star Program (No.03QA14036) ;The Special Funds for Major Specialties of Shanghai Education Committee.

摘　　要：This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关 键 词：Singular perturbation Θ-METHODS DISSIPATIVITY Exponential stability. 

分 类 号：O175.13[理学—数学]