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The stability theory of difference schemes is mostly a linear theory. To understand the behaviour of difference schemes on nonlinear differential equations, it seems desirable to extend the stability theory into a nonlinear theory. As a step in that direction, the stability properties of Euler-related integration algorithms are investigated by checking how they preserve or violate the dynamical structure of the logistic differential equation. It is found that partially implicit schemes are superior to explicit schemes when they are stable and the blow-up time has not passed. When such a rational scheme turns unstable, however, it has much less desirable properties than explicit schemes. A map has been produced showing two branches of stable fixed points. Both of them lose stability to a Feigenbaum sequence of period doubling bifurcations and chaotic trajectories independently of each other.

Additional information

Authors: GROTE K, Max-Planck-Institut für Plasmaphysik, Garching bei München (DE);MEYER-SPASCHE R, Max-Planck-Institut für Plasmaphysik, Garching bei München (DE)
Bibliographic Reference: Report: IPP 6/330 EN (1995) 24 pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 8046 Garching bei München (DE)
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