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MiS Preprint

Numerical attractors for rough differential equations

Hoang Duc Luu and Peter Kloeden


We study the explicit Euler scheme to approximate the solutions of rough differential equations under a bounded or linear diffusion term, where the drift term satisfies a local Lipschitz continuity and a bounded linear growth condition. The Euler scheme is then proved to converge for a given solution, although the approximation of the error depends on the initial condition. For a dissipative drift term with linear growth condition and a bounded diffusion term, the numerical solution under a regular grid generates a random dynamical system which admits a random pullback attractor. We also prove that for bounded drift and diffusion terms, the numerical pullback attractor then converges upper semi-continuously to the continuous-time pullback attractor as the time step goes to zero.

rough differential equations, Euler scheme, random dynamical systems, random attractors

Related publications

2023 Repository Open Access
Hoang Duc Luu and Peter E. Kloeden

Numerical attractors for rough differential equations

In: SIAM journal on numerical analysis, 61 (2023) 5, pp. 2011-2508