Asymptotic Behavior of an Adapted Implicit Discretization of Slowly Damped Second Order Dynamical Systems

被引：0

作者：

Horsin, Thierry ^{[1
]}

Jendoubi, Mohamed Ali ^{[2
,3
]}

机构：

[1] CNAM, EA7340, Lab M2N, 2 rue Conte, F-75003 Paris, France

[2] Univ Carthage, Inst Preparatoire Etud Sci & Tech, BP 51, La Marsa 2070, Tunisia

[3] Univ Tunis El Manar, Fac Sci Tunis, Lab Equat aux Der Partielles, LR03ES04, Tunis 2092, Tunisia

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2023年 / 88卷 / 02期

关键词：

Descent methods; Real analytic functions; Lojasiewicz gradient inequality; Single limit-point convergence; Stability; Asymptotically small dissipation; Convergence rates; Variable time-step discretization; Implicit scheme; Slow damping; GRADIENT-LIKE SYSTEMS; CONVERGENCE; EQUATIONS; EQUILIBRIUM;

D O I：

10.1007/s00245-023-10027-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the context of damped second order linear dynamical systems, we study the asymptotic behavior of a time discretization of a slowly damped differential equation. We prove that this discretization can be constructed by means of a variable time step that gives rise to the same asymptotic behaviour as for the system in continuous time.

引用

页数：26

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