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IMA Journal of Numerical Analysis 2001 21(3):733-749; doi:10.1093/imanum/21.3.733
© 2001 by Institute of Mathematics and its Applications
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Numerical flow-box theorems under structural assumptions

Barnabas M. Garay1 and Peter L. Simon2

1 Department of Mathematics, University of Technology, H-1521 Budapest, Hungary. Email: garay@math.bme.hu 2 Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary. Email: simonp@cs.elte.hu

The numerical flow-box theorem says that locally, in the vicinity of nonequilibria, discretized solutions of an autonomous ordinary differential equation are exact solutions of a modified equation nearby: for stepsize h sufficiently small the original discretization operator is the time–h map of the solution operator of the modified equation. It is shown that the very same result holds true in the following categories of differential equations and discretizations:

I/ preserving a finite number of first integrals;

V/ preserving the volume form;

S/ preserving the canonical symplectic form.

Key Words: flow-; box; perfectly modified equation; symplectic discretization


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