Hyperasymptotics for nonlinear ODEs I. A Riccati equation-Reference-Cited by-同舟云学术

Hyperasymptotics for nonlinear ODEs I. A Riccati equation

Published:2005-06-24 Issue:2060 Volume:461 Page:2503-2520
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Olde Daalhuis A.B¹

Affiliation:

1. School of Mathematics, King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ, UK

Abstract

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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2005.1462

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