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A solution to Meneguette's polynomial problem

Year: 2026

Type: preprint

Abstract: In 1979, Jeltsch [Numer. Math. 32 (1979), 167-181] conjectured that every zero-stable Brown method is stiffly stable. For Brown $(K,L)$ methods, Meneguette subsequently reduced the relevant $A_0$-stability question to a zero-location property for a family of perturbed characteristic polynomials. A closely related perturbation question already appeared in his 1987 Oxford doctoral thesis, and he later posed a broader purely polynomial version of the problem in 1994 [SIAM Review 36 (1994), 656-657]. We provide a complete solution to Meneguette's polynomial problem.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.20226

Author: Castillo, K.

Institution: University of Coimbra

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Universidade de Coimbra, Fundação para a Ciência e a Tecnologia, Centro de Matemática, Universidade de Coimbra

Awards: G3204329492, Centro de Matemática da Universidade de Coimbra, A Functional Approach to Special Functions and Orthogonal Polynomials, G461020795, G5712257541, G6265307419, G6997658380, Centro de Matemática da Universidade de Coimbra, G8985288032

OpenAlex ID: W7170176002

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