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Zbl 1186.34076
Olde Daalhuis, A.B.
Hyperasymptotics for nonlinear ODEs. I: A Riccati equation. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 461, No. 2060, 2503-2520 (2005). ISSN 1364-5021; ISSN 1471-2946/e

Summary: We illustrate how one can obtain hyperasymptotic expansions for solutions of nonlinear ordinary differential equations. The example is a Riccati equation. The main tools that we need are transseries expansions and the Riemann sheet structure of the Borel transform of the divergent asymptotic expansions. Hyperasymptotic expansions determine the solutions uniquely. A numerical illustration is included.

MSC 2000:: *34E05 Asymptotic expansions (ODE)

Keywords: asymptotic expansions; hyperasymptotics; nonlinear differential equations; Riccati equation; Stokes phenomenon; transseries

Cited in: Zbl 1206.34077

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