Preference and Stability Regions for Semi-Implicit Composition Schemes

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...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 22; p. 4327
Main Authors Fedoseev, Petr, Karimov, Artur, Legat, Vincent, Butusov, Denis
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.11.2022
Subjects
Accuracy
Algorithms
Composition
composition method
Eigenvalues
Investigations
Mathematical research
Methods
Numerical analysis
Numerical integration
Numerical methods
Numerical stability
ODE
semi-implicit method
Stability analysis
stability regions
United States
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10224327