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RESEARCH PRODUCT

A Unifying Framework for Perturbative Exponential Factorizations

Fernando CasasCristina ChiraltJ A OteoAna Arnal

subject

Differential equationGeneral MathematicsEquacions diferencials01 natural sciencesUpper and lower bounds010305 fluids & plasmas0103 physical sciencesConvergence (routing)Fer expansionComputer Science (miscellaneous)Applied mathematicsZassenhaus formula010306 general physicsEngineering (miscellaneous)Mathematicslcsh:MathematicsBellman problemWilcox expansionOrder (ring theory)lcsh:QA1-939Exponential functionTransformation (function)sequences of linear transformationsProduct (mathematics)Scheme (mathematics)Matemàtica

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 theWilcox 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.

yearjournalcountryeditionlanguage
2021-03-17Mathematics
10.3390/math9060637http://dx.doi.org/10.3390/math9060637