Numerical validation of blow-up solutions of ordinary differential equations

2016/06/09 by Akitoshi Takayasu, Kaname Matsue, Takayasu, Akitoshi +9
Computer Science · Mathematics · Physics and Astronomy · #34C08 #35B44 #37B25 #65L99 #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1606.03039

openalex publication_date 2016/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• On the construction of Lyapunov functions with computer assistance

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