Preference and Stability Regions for Semi-Implicit Composition Schemes

Petr Fedoseev, Artur Karimov, Vincent Legat, Denis Butusov
2022 Mathematics  
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
more » ... 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.
doi:10.3390/math10224327 fatcat:fgzueswajrdojdklc3w4wiqqcy