 Numerical attractors and approximations for stochastic or deterministic sine-Gordon lattice equationsShuang Yang and Yangrong Li Applied Mathematics and Computation, 2022, vol. 413, issue C Abstract: First, we apply the implicit Euler scheme to discretize the sine-Gordon lattice equation (possessing a global attractor) and prove the existence of a numerical attractor for the time-discrete sine-Gordon lattice system with small step sizes. Second, we establish the upper semi-convergence from the numerical attractor towards the global attractor when the step size tends to zero. Third, we establish the upper semi-convergence from the random attractor of the stochastic sine-Gordon lattice equation to the global attractor when the intensity of noise goes to zero. Fourth, we show the finitely dimensional approximations of the three (numerical, random and global) attractors as the dimension of the state space goes to infinity. In a word, we establish four paths of convergence of finitely dimensional (numerical and random) attractors towards the global attractor. Keywords: Sine-Gordon lattice; Implicit euler scheme; Numerical attractor; Random attractor; Finite-dimensional approximation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321007244 DOI: 10.1016/j.amc.2021.126640 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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