Numerical validation of blow-up solutions of ordinary differential equations
Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka,, Makoto Mizuguchi, Shin'ichi Oishi
TL;DR
This paper introduces a validated numerical method for confirming blow-up solutions and their blow-up times in ordinary differential equations using compactifications, Lyapunov functions, and interval arithmetic, demonstrated through numerical examples.
Contribution
The paper presents a novel approach combining compactifications, Lyapunov functions, and interval arithmetic for validating blow-up solutions and times in ODEs.
Findings
Method successfully validates blow-up solutions.
Applicable to various numerical examples.
Provides rigorous bounds on blow-up times.
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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Taxonomy
TopicsModel Reduction and Neural Networks · Numerical Methods and Algorithms · Numerical methods for differential equations