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On Roots and Error Constants of Optimal Stability Polynomials

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Abstract

Optimal stability polynomials are polynomials whose stability region is as large as possible in a certain region, here the negative real axis. We are interested in such polynomials which in addition, obey a certain order condition. An important application of these polynomials is the construction of stabilized explicit Runge-Kutta methods. In this paper we will give some properties of the roots of these polynomials, and prove that their error constant is always positive. Furthermore, for a given order, the error constant decreases as the degree increases.

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  1. Département de Mathématiques, Université de Genève, Case postale 240, CH-1211, Genève 24, Switzerland.

    Assyr Abdulle

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  1. Assyr Abdulle
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Abdulle, A. On Roots and Error Constants of Optimal Stability Polynomials. BIT Numerical Mathematics 40, 177–182 (2000). https://doi.org/10.1023/A:1022378621048

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  • DOI: https://doi.org/10.1023/A:1022378621048

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