Averaging of ordinary differential equations with slowly varying averages

Pages: 353 - 365, Volume 14, Issue 2, September 2010

doi:10.3934/dcdsb.2010.14.353       Abstract        Full Text (190.9K)       Related Articles

Zvi Artstein - Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel (email)

Abstract: 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.

Keywords:  Averaging, time-varying differential equations, varying averages.
Mathematics Subject Classification:  Primary: 34C29.

Received: July 2009;      Revised: November 2009;      Published: June 2010.