Preference and Stability Regions for Semi-Implicit Composition Schemes

Autor: Petr Fedoseev, Artur Karimov, Vincent Legat, Denis Butusov
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Mathematics, Vol 10, Iss 22, p 4327 (2022)
Druh dokumentu: article
ISSN: 10224327
2227-7390
DOI: 10.3390/math10224327
Popis: A numerical stability region is a valuable tool for estimating the practical applicability of numerical methods and comparing them in terms of stability. However, only a little information can be obtained from the stability regions when their shape is highly irregular. Such irregularity is inherent to many recently developed semi-implicit and semi-explicit methods. In this paper, we introduce a new tool for analyzing numerical methods called preference regions. This allows us to compare various methods and choose the appropriate stepsize for their practical implementation, such as stability regions, but imposes stricter conditions on the methods, and therefore is more accurate. We present a thorough stability and preference region analysis for a new class of composition methods recently proposed by F. Casas and A. Escorihuela-Tomàs. We explicitly show how preference regions, plotted for an arbitrary numerical integration method, complement the conventional stability analysis and offer better insights into the practical applicability of the method.
Databáze: Directory of Open Access Journals
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