A Unifying Framework for Perturbative Exponential Factorizations

A Unifying Framework for Perturbative Exponential Factorizations

We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed....

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Main Authors: Ana Arnal, Fernando Casas, Cristina Chiralt, José Angel Oteo
Format: Article
Language:English
Published: MDPI AG 2021-03-01
Series:Mathematics
Subjects:
sequences of linear transformations
Wilcox expansion
Fer expansion
Zassenhaus formula
Bellman problem
Online Access:https://www.mdpi.com/2227-7390/9/6/637
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spelling doaj-0cbbc494502d4950a5d1aca808751de12021-03-18T00:00:55ZengMDPI AGMathematics2227-73902021-03-01963763710.3390/math9060637A Unifying Framework for Perturbative Exponential FactorizationsAna Arnal0Fernando Casas1Cristina Chiralt2José Angel Oteo3Departament de Matemàtiques and IMAC, Universitat Jaume I, 12071 Castellón, SpainDepartament de Matemàtiques and IMAC, Universitat Jaume I, 12071 Castellón, SpainDepartament de Matemàtiques and IMAC, Universitat Jaume I, 12071 Castellón, SpainDepartament de Física Teòrica, Universitat de València and Institute for Integrative Systems Biology (I2SysBio), 46100 Burjassot, SpainWe propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed. A new lower bound for the convergence of the Wilcox expansion is provided, as well as some applications of the results. In particular, two examples are worked out up to a high order of approximation to illustrate the behavior of the Wilcox expansion.https://www.mdpi.com/2227-7390/9/6/637sequences of linear transformationsWilcox expansionFer expansionZassenhaus formulaBellman problem
collection DOAJ
language English
format Article
sources DOAJ
author Ana Arnal
Fernando Casas
Cristina Chiralt
José Angel Oteo
spellingShingle Ana Arnal
Fernando Casas
Cristina Chiralt
José Angel Oteo
A Unifying Framework for Perturbative Exponential Factorizations
Mathematics
sequences of linear transformations
Wilcox expansion
Fer expansion
Zassenhaus formula
Bellman problem
author_facet Ana Arnal
Fernando Casas
Cristina Chiralt
José Angel Oteo
author_sort Ana Arnal
title A Unifying Framework for Perturbative Exponential Factorizations
title_short A Unifying Framework for Perturbative Exponential Factorizations
title_full A Unifying Framework for Perturbative Exponential Factorizations
title_fullStr A Unifying Framework for Perturbative Exponential Factorizations
title_full_unstemmed A Unifying Framework for Perturbative Exponential Factorizations
title_sort unifying framework for perturbative exponential factorizations
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-03-01
description We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed. A new lower bound for the convergence of the Wilcox expansion is provided, as well as some applications of the results. In particular, two examples are worked out up to a high order of approximation to illustrate the behavior of the Wilcox expansion.
topic sequences of linear transformations
Wilcox expansion
Fer expansion
Zassenhaus formula
Bellman problem
url https://www.mdpi.com/2227-7390/9/6/637
work_keys_str_mv AT anaarnal aunifyingframeworkforperturbativeexponentialfactorizations
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AT anaarnal unifyingframeworkforperturbativeexponentialfactorizations
AT fernandocasas unifyingframeworkforperturbativeexponentialfactorizations
AT cristinachiralt unifyingframeworkforperturbativeexponentialfactorizations
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