Numerische Mathematik

, Volume 52, Issue 6, pp 605–619

Stability analysis of one-step methods for neutral delay-differential equations

  • A. Bellen
  • Z. Jackiewicz
  • M. Zennaro

DOI: 10.1007/BF01395814

Cite this article as:
Bellen, A., Jackiewicz, Z. & Zennaro, M. Numer. Math. (1988) 52: 605. doi:10.1007/BF01395814


In this paper stability properties of one-step methods for neutral functional-differential equations are investigate. Stability regions are characterized for Runge-Kutta methods with respect to the linear test equation
$$\begin{gathered} y'\left( t \right) = ay\left( t \right) + by\left( {t - \tau } \right) + cy'\left( {t - \tau } \right),t \geqq 0, \hfill \\ y\left( t \right) = g\left( t \right), - \tau \leqq t \leqq 0, \hfill \\ \end{gathered} $$
τ>0, where,a, b, andc are complex parameters. In particular, it is shown that everyA-stable collocation method for ordinary differential equations can be extended to a method for neutrals delay-differential equations with analogous stability properties (the so called NP-stable method). We also investigate how the approximation to the derivative of the solution affects stability properties of numerical methods for neutral equations.

Subject Classifications

AMS(MOS): 65L20CR: G1.7

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • A. Bellen
    • 1
  • Z. Jackiewicz
    • 2
  • M. Zennaro
    • 1
  1. 1.Dipartimento di Scienzes MatematicheUniversita degli Studi di TriesteTriesteItaly
  2. 2.Department of MathematicsArizona State UniversityTempeUSA