Some issues with the numerical treatment of delay differential equations

A. S. Eremin, A. R. Humphries, A. A. Lobaskin

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

In this paper several problems arising when implementing methods to numerically solve delay-differential equations, such as overlapping, difficulties with error estimation, discontinuities of solution derivatives and the detection of such discontinuity points, are considered. Several approaches to each issue are discussed. The best solutions for explicit and diagonally implicit Runge-Kutta methods for DDEs are reported. A numerical comparison between a method implementing the handling of such problems, and the Matlab code ddesd, demonstrates that our method is more efficient.

Original languageEnglish
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019
EditorsTheodore E. Simos, Charalambos Tsitouras
PublisherAmerican Institute of Physics
ISBN (Electronic)9780735440258
DOIs
StatePublished - 24 Nov 2020
EventInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 - Rhodes, Greece
Duration: 23 Sep 201928 Sep 2019

Publication series

NameAIP Conference Proceedings
Volume2293
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019
CountryGreece
CityRhodes
Period23/09/1928/09/19

Scopus subject areas

  • Physics and Astronomy(all)
  • Mathematics(all)

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