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- Title
Semi-Discretized Approximation of Stability of Sine-Gordon System with Average-Central Finite Difference Scheme.
- Authors
Wang, Xudong; Wang, Sizhe; Qiao, Xing; Zheng, Fu
- Abstract
In this study, the energy control and asymptotic stability of the 1D sine-Gordon equation were investigated from the viewpoint of numerical approximation. An order reduction method was employed to transform the closed-loop system into an equivalent system, and an average-central finite difference scheme was constructed. This scheme is not only energy-preserving but also possesses uniform stability. The discrete multiplier method was utilized to obtain the uniformly asymptotic stability of the discrete systems. Moreover, to cope with the nonlinear term of the model, a discrete Wirtinger inequality suitable for our approximating scheme was established. Finally, several numerical experiments based on the eigenvalue distribution of the linearized approximation systems were conducted to demonstrate the effectiveness of the numerical approximating algorithm.
- Subjects
FINITE differences; DISCRETE systems; CLOSED loop systems; EIGENVALUES; SPEED
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 16, p2592
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12162592