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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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/22/4327 |
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| author | Petr Fedoseev Artur Karimov Vincent Legat Denis Butusov |
| author_facet | Petr Fedoseev Artur Karimov Vincent Legat Denis Butusov |
| author_sort | Petr Fedoseev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T18:10:38Z |
| format | Article |
| id | doaj.art-340720e528434d9f89a36b98229bc1b9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:10:38Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-340720e528434d9f89a36b98229bc1b92023-11-24T09:09:48ZengMDPI AGMathematics2227-73902022-11-011022432710.3390/math10224327Preference and Stability Regions for Semi-Implicit Composition SchemesPetr Fedoseev0Artur Karimov1Vincent Legat2Denis Butusov3Department of Computer-Aided Design, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, RussiaYouth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, RussiaInstitute of Mechanics, Materials and Civil Engineering (IMMC), Université catholique de Louvain, 1348 Louvain-la-Neuve, BelgiumYouth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, RussiaA 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.https://www.mdpi.com/2227-7390/10/22/4327ODEnumerical integrationcomposition methodsemi-implicit methodstability regions |
| spellingShingle | Petr Fedoseev Artur Karimov Vincent Legat Denis Butusov Preference and Stability Regions for Semi-Implicit Composition Schemes Mathematics ODE numerical integration composition method semi-implicit method stability regions |
| title | Preference and Stability Regions for Semi-Implicit Composition Schemes |
| title_full | Preference and Stability Regions for Semi-Implicit Composition Schemes |
| title_fullStr | Preference and Stability Regions for Semi-Implicit Composition Schemes |
| title_full_unstemmed | Preference and Stability Regions for Semi-Implicit Composition Schemes |
| title_short | Preference and Stability Regions for Semi-Implicit Composition Schemes |
| title_sort | preference and stability regions for semi implicit composition schemes |
| topic | ODE numerical integration composition method semi-implicit method stability regions |
| url | https://www.mdpi.com/2227-7390/10/22/4327 |
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