, Volume 52, Issue 6, pp 605-619

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

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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.

The work was supported by the Italian Government from M.P.I. funds, 40%
The work was partially supported by Consiglio Nazionale dell Ricerche and by the National Science Foundation under grant NSF DMS-852090