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September  2010, 14(2): 353-365. doi: 10.3934/dcdsb.2010.14.353

Averaging of ordinary differential equations with slowly varying averages

1. 

Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel

Received  July 2009 Revised  November 2009 Published  June 2010

The averaging method asserts that a good approximation to the solution of a time varying ordinary differential equation with small amplitude is the solution of the averaged equation, and that the error is maintained small on a long time interval. We establish a similar result allowing the averaged equation to vary in time, thus allowing slowly varying averages of the original equation. Both the modeling issue and the estimation of the resulting errors are addressed.
Citation: Zvi Artstein. Averaging of ordinary differential equations with slowly varying averages. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 353-365. doi: 10.3934/dcdsb.2010.14.353
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