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IMA Journal of Numerical Analysis 2003 23(2):221-239; doi:10.1093/imanum/23.2.221
© 2003 by Institute of Mathematics and its Applications
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Uniform attractors of nonautonomous index 2 differential algebraic equations under discretization

Peter E. Kloeden1 and Johannes Schropp2

1 FB Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main, Germany 2 FB Mathematik und Statistik, Universität Konstanz, D-78434 Konstanz, Germany

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.

Key Words: index 2; differential algebraic equation; Runge–Kutta method; nonautonomous dynamical system

Received 21 September 2001. Revised 26 August 2002.


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