A Unifying Framework for Perturbative Exponential Factorizations

Ana Arnal, Fernando Casas, Cristina Chiralt and José Angel Oteo
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Ana Arnal: Departament de Matemàtiques and IMAC, Universitat Jaume I, 12071 Castellón, Spain
Fernando Casas: Departament de Matemàtiques and IMAC, Universitat Jaume I, 12071 Castellón, Spain
Cristina Chiralt: Departament de Matemàtiques and IMAC, Universitat Jaume I, 12071 Castellón, Spain
José Angel Oteo: Departament de Física Teòrica, Universitat de València and Institute for Integrative Systems Biology (I2SysBio), 46100 Burjassot, Spain

Mathematics, 2021, vol. 9, issue 6, 1-21

Abstract: 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.

Keywords: sequences of linear transformations; Wilcox expansion; Fer expansion; Zassenhaus formula; Bellman problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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