Numerical attractors and approximations for stochastic or deterministic sine-Gordon lattice equations

作者：

Highlights：

• A numerical attractor for the time-discrete sine-Gordon lattice equation via the implicit Euler scheme is obtained.

• Upper semi-convergence of numerical attractors towards to the global attractor is established.

• Upper semi-convergence of random attractors for the stochastic sine-Gordon lattice is proved.

• Finitely dimensional approximations of the three (numerical, random and global) attractors are shown.

• Four paths of convergence of finitely dimensional (numerical and random) attractors towards the global attractor are established.

摘要

•A numerical attractor for the time-discrete sine-Gordon lattice equation via the implicit Euler scheme is obtained.•Upper semi-convergence of numerical attractors towards to the global attractor is established.•Upper semi-convergence of random attractors for the stochastic sine-Gordon lattice is proved.•Finitely dimensional approximations of the three (numerical, random and global) attractors are shown.•Four paths of convergence of finitely dimensional (numerical and random) attractors towards the global attractor are established.

论文关键词：Sine-Gordon lattice,Implicit euler scheme,Numerical attractor,Random attractor,Finite-dimensional approximation

论文评审过程：Received 19 April 2021, Revised 3 August 2021, Accepted 27 August 2021, Available online 6 September 2021, Version of Record 6 September 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126640