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Uniform attractors of nonautonomous index 2 differential algebraic equations under discretization

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2003

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Kloeden, Peter E.

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https://doi.org/10.1093/imanum/23.2.221
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IMA Journal of Numerical Analysis. 2003, 23(2), pp. 221-239. ISSN 0272-4979. eISSN 1464-3642. Available under: doi: 10.1093/imanum/23.2.221

Zusammenfassung

The long‐time behaviour of Runge–Kunge discretizations is investigated when applied to a smooth nonautonomous index 2 differential algebraic equation (DAE) with a cocycle structure, i.e. a DAE driven by an autonomous dynamical system, which is assumed to have a uniform attractor. It is shown that the cocycle structure of the continuous dynamics is preserved under discretization and that a uniform forward or pullback attractor of the DAE persists under discretization by a Runge–Kutta scheme with the component subsets of the numerical attractor converging upper semicontinuously to their continuous time counterparts.

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510 Mathematik

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ISO 690KLOEDEN, Peter E., Johannes SCHROPP, 2003. Uniform attractors of nonautonomous index 2 differential algebraic equations under discretization. In: IMA Journal of Numerical Analysis. 2003, 23(2), pp. 221-239. ISSN 0272-4979. eISSN 1464-3642. Available under: doi: 10.1093/imanum/23.2.221
BibTex
@article{Kloeden2003-04-01Unifo-43195,
  year={2003},
  doi={10.1093/imanum/23.2.221},
  title={Uniform attractors of nonautonomous index 2 differential algebraic equations under discretization},
  number={2},
  volume={23},
  issn={0272-4979},
  journal={IMA Journal of Numerical Analysis},
  pages={221--239},
  author={Kloeden, Peter E. and Schropp, Johannes}
}
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