Stability analysis of two-step Runge-Kutta methods for delay differential equations

Z. Bartoszewski, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We investigate stability properties of two-step Runge-Kutta methods with respect to the linear test equation y′(t) = ay(t) + by (t - ρ), t ≥ 0, y(t) = g(t), t ∈ [-ρ,0], where a and b are complex parameters. It is known that the solution y(t) to this equation tends to zero at t → ∞ if |b| < - Re(a). We will show that under some conditions this property is inherited by any A-stable two-step Runge-Kutta method applied on a constrained mesh to delay differential equations, i.e., that the corresponding method is P-stable.

Original languageEnglish (US)
Pages (from-to)83-93
Number of pages11
JournalComputers and Mathematics with Applications
Issue number1-2
StatePublished - Jul 2002

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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