English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

For singular perturbation problems in dynamical systems, various appropriatesingular perturbation methods have been proposed to eliminate secular termsappearing in the naive expansion. For example, the method of multiple timescales, the normal form method, center manifold theory, the renormalizationgroup method are well known. In this paper, it is shown that all of thesolutions of the reduced equations constructed with those methods are exactlyequal to sum of the most divergent secular terms appearing in the naiveexpansion. For the proof, a method to construct a perturbation solution whichdiffers from the conventional one is presented, where we make use of the theoryof Lie symmetry group.

Solution of reduced equations derived with singular perturbation methods