Numerical validation of blow-up solutions of ordinary differential equations
Numerical Analysis
2016-11-09 v2 Dynamical Systems
Abstract
This paper focuses on blow-up solutions of ordinary differential equations (ODEs). We present a method for validating blow-up solutions and their blow-up times, which is based on compactifications and the Lyapunov function validation method. The necessary criteria for this construction can be verified using interval arithmetic techniques. Some numerical examples are presented to demonstrate the applicability of our method.
Keywords
Cite
@article{arxiv.1606.03039,
title = {Numerical validation of blow-up solutions of ordinary differential equations},
author = {Akitoshi Takayasu and Kaname Matsue and Takiko Sasaki and Kazuaki Tanaka and Makoto Mizuguchi and Shin'ichi Oishi},
journal= {arXiv preprint arXiv:1606.03039},
year = {2016}
}
Comments
Accepted version, to appear in Journal of Computational and Applied Mathematics