Dual approach to averaged values of functions: A form for weighting coefficient

Abstract

Averaged values play major roles in the study of dynamic processes. The use of those values allows transforming varying processes to some constant characteristics that are much easier to be investigated. In order to extend the use of averaged values one may apply the dual approach which suggests a consideration of two different aspects of a problem in question. In this short communication the main idea of the dual conception is further extended to suggest a new form for weighting coefficient and then a new averaged value of functions. This new averaged value depends on the parameter \(s\) and contains the classical averaged value when \(s=0\). In the example of Duffing oscillator it is shown that the parameter \(s\) can be chosen as \(s=n/(2\pi)\) and for \(n=4\) one gets the solution that is much accurate than the conventional one obtained by the classical criterion of equivalent linearization.