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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Bibliographic Details
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
Description
Summary: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.
ISSN:2227-7390

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