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

In this paper we study linear projection methods for approximating thesolution and simultaneously preserving first integrals of autonomous ordinarydifferential equations. We show that (linear) projection methods are a subsetof discrete gradient methods. In particular, each projection method isequivalent to a class of discrete gradient methods (where the choice ofdiscrete gradient is arbitrary) and earlier results for discrete gradientmethods also apply to projection methods. Thus we prove that for the case ofpreserving one first integral, under certain mild conditions, the numericalsolution for a projection method exists and is locally unique, and preservesthe order of accuracy of the underlying method.  In the case of preserving multiple first integrals the relationship betweenprojection methods and discrete gradient methods persists. Moreover, numericalexamples show that similar existence and order results should also hold for themultiple integral case.  For completeness we show how existing projection methods from the literaturefit into our general framework.

Projection methods and discrete gradient methods for preserving first integrals of ODEs