Numerical dynamics for discrete nonlinear damping Korteweg–de Vries equations

Guifen Liu, Yangrong Li and Fengling Wang

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 225, issue C, 332-349

Abstract: We study the numerical scheme of both solution and attractor for the time-space discrete nonlinear damping Korteweg–de Vries (KdV) equation, which is neither conservative nor coercive. First, we establish a new Taylor expansion as well as a global attractor for the KdV lattice system. Second, we prove the unique existence of numerical solution as well as numerical attractor for the discrete-time KdV lattice system via the implicit Euler scheme. Third, we estimate the discretization error and interpolation error between continuous-time and discrete-time solutions, and then establish the upper semi-convergence from numerical attractors to the global attractor as the time-size tends to zero. Fourth, we establish the finitely dimensional approximation of numerical attractors. Finally, we establish the upper bound as well as the lower semi-convergence of numerical attractors with respect to the external force and the damping constant.

Keywords: Discrete kdV equations; Implicit Euler scheme; Numerical solutions; Numerical attractors; Semicontinuity of attractors (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:225:y:2024:i:c:p:332-349

DOI: 10.1016/j.matcom.2024.05.025

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