Numerical Approach to Painlev\'e Transcendents on Unbounded Domains
Classical Analysis and ODEs
2018-07-13 v1 Mathematical Physics
math.MP
Numerical Analysis
Abstract
A multidomain spectral approach for Painlev\'e transcendents on unbounded domains is presented. This method is designed to study solutions determined uniquely by a, possibly divergent, asymptotic series valid near infinity in a sector and approximates the solution on straight lines lying entirely within said sector without the need of evaluating truncations of the series at any finite point. The accuracy of the method is illustrated for the example of the tritronqu\'ee solution to the Painlev\'e I equation.
Keywords
Cite
@article{arxiv.1807.04442,
title = {Numerical Approach to Painlev\'e Transcendents on Unbounded Domains},
author = {Christian Klein and Nikola Stoilov},
journal= {arXiv preprint arXiv:1807.04442},
year = {2018}
}