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Global dynamical properties of Euler and backward Euler

Published online by Cambridge University Press:  19 September 2008

Kevin Hockett
Kevin Hockett
Affiliation:
Department of Mathematics, The George Washington University, Washington, DC 20052, USA
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Abstract

We investigate the global dynamics of both the Euler and backward Euler algorithms as applied to polynomial vector fields on the Riemann sphere = ℂ ∪ {∞}. The geometry and dynamics of solutions at infinity is seen to play an important role in organizing the global dynamics of the flow, and we show how to modify both algorithms to account for this structure, thereby obtaining global approximations to the flow.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 4 , December 1993 , pp. 675 - 696
Copyright
Copyright © Cambridge University Press 1993

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