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| Titel: |
Cocycle Attractors of Variable Time-Step Discretizations of Lorenzian Systems |
| Auteur: |
Kloeden, P. E. Schmalfuss, B. |
| Verschenen in: |
Journal of difference equations and applications |
| Paginering: | Jaargang 3 (1997) nr. 2 pagina's 125-145 |
| Jaar: |
1997 |
| Inhoud: |
Variable time-step numerical schemes applied to an autonomous differential equation generate cocycles rather than semigroups, so their asymptotic behaviour must be described in terms of cocycle attractors consisting of an equivariant family of sets in contrast to the single invariant set forming the attractor of a constant time-step scheme. The existence of such cocycle attractors is established here for a special linear-implicit versio of the Euler scheme with variable time-steps that is applied to a class of autonomous linear-quadratic differential equations of similar structure to the Lorenz equations. The relationship between the numerical cocycle attractors and the original global attractor of the differential equation is also investigated. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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