Article

Numerische Mathematik

, Volume 52, Issue 6, pp 605-619

First online:

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

  • A. BellenAffiliated withDipartimento di Scienzes Matematiche, Universita degli Studi di Trieste
  • , Z. JackiewiczAffiliated withDepartment of Mathematics, Arizona State University
  • , M. ZennaroAffiliated withDipartimento di Scienzes Matematiche, Universita degli Studi di Trieste

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Summary

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): 65L20 CR: G1.7