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
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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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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DOI: https://doi.org/10.1007/BF01395814