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IOD-type continuity-sets and bounds of numerical attractors for discrete Klein–Gordon–Schrödinger equations

Author

Listed:
  • Li, Yangrong
  • Wang, Zhiqiang
  • Tang, Xiaowen

Abstract

Discrete-time Klein–Gordon–Schrödinger lattice equations are established according to implicit Euler schemes, while a family of numerical attractors is obtained when time-sizes belong to an existing interval. The continuity-set of numerical attractors under the Hausdorff distance is shown to be a dense IOD-type (Intersection of countably many Open Dense sets) in the existing interval, moreover, this continuity-set has the continuum cardinality. A common bound of all numerical attractors is provided and leads to the continuous convergence of numerical attractors as two external forces tend to zero. Finally, the global attractor of the original continuous-time system is approximated by numerical attractors in the sense of upper semicontinuity. Forward invariant sets, recursive tails estimates and Taylor’s remainders play key roles in the proofs.

Suggested Citation

  • Li, Yangrong & Wang, Zhiqiang & Tang, Xiaowen, 2026. "IOD-type continuity-sets and bounds of numerical attractors for discrete Klein–Gordon–Schrödinger equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 242(C), pages 19-35.
    • Handle: RePEc:eee:matcom:v:242:y:2026:i:c:p:19-35
    DOI: 10.1016/j.matcom.2025.11.015
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