Formal and numerical computations with resurgent functions

Formal and numerical computations with resurgent functions

We establish resurgence properties for solutions of linear ordinary differential equations with polynomial coefficients, at an irregular–singular point of rank one and derive resurgence relations when applying alien derivations to these solutions. Explicit calculations, formal and numerical, are giv...

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Veröffentlicht in:Numerical algorithms 2005-12, Vol.40 (4), p.323-353
Hauptverfasser: Fauvet, F., Thomann, J.
Format: Artikel
Sprache:eng
Schlagworte:
Differential equations
Polynomials
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Beschreibung
Zusammenfassung:We establish resurgence properties for solutions of linear ordinary differential equations with polynomial coefficients, at an irregular–singular point of rank one and derive resurgence relations when applying alien derivations to these solutions. Explicit calculations, formal and numerical, are given for several examples.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-005-5326-5