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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.

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Authors and Affiliations

  1. Dipartimento di Scienzes Matematiche, Universita degli Studi di Trieste, I-34100, Trieste, Italy

    A. Bellen & M. Zennaro

  2. Department of Mathematics, Arizona State University, 85287, Tempe, AZ, USA

    Z. Jackiewicz

Authors
  1. A. Bellen
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  2. Z. Jackiewicz
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  3. M. Zennaro
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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

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Bellen, A., Jackiewicz, Z. & Zennaro, M. Stability analysis of one-step methods for neutral delay-differential equations. Numer. Math. 52, 605–619 (1988). https://doi.org/10.1007/BF01395814

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