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arXiv · 1606.03039

Numerical validation of blow-up solutions of ordinary differential equations

Akitoshi Takayasu·Kaname Matsue·Takiko Sasaki·Kazuaki Tanaka·Makoto Mizuguchi·Shin'ichi Oishi
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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.

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Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shin'ichi Oishi. 2016-11-08. Numerical validation of blow-up solutions of ordinary differential equations. https://arxiv.org/abs/1606.03039

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