Discrete variable methods for delay-differential equations with threshold-type delays

Zdzislaw Jackiewicz, B. Zubik-Kowal

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We study numerical solution of systems of delay-differential equations in which the delay function, which depends on the unknown solution, is defined implicitly by the threshold condition. We study discrete variable numerical methods for these problems and present error analysis. The global error is composed of the error of solving the differential systems, the error from the threshold conditions and the errors in delay arguments. Our theoretical analysis is confirmed by numerical experiments on threshold problems from the theory of epidemics and from population dynamics.

Original languageEnglish (US)
Pages (from-to)514-523
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume228
Issue number2
DOIs
StatePublished - Jun 15 2009

Fingerprint

Discrete Variables
Delay Differential Equations
Differential equations
Population dynamics
Population Dynamics
Error Analysis
Differential System
Error analysis
Numerical methods
Theoretical Analysis
Numerical Methods
Numerical Experiment
Numerical Solution
Unknown
Experiments

Keywords

  • Delay-differential systems
  • Error analysis
  • Numerical approximations
  • Threshold conditions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Discrete variable methods for delay-differential equations with threshold-type delays. / Jackiewicz, Zdzislaw; Zubik-Kowal, B.

In: Journal of Computational and Applied Mathematics, Vol. 228, No. 2, 15.06.2009, p. 514-523.

Research output: Contribution to journalArticle

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