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A Unifying Framework for Perturbative Exponential Factorizations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ana Arnal & Fernando Casas & Cristina Chiralt & José Angel Oteo, 2021. "A Unifying Framework for Perturbative Exponential Factorizations," Mathematics, MDPI, vol. 9(6), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:637-:d:518706
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