Numerical validation of blow-up solutions of ordinary differential equations

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.

Accepted version, to appear in Journal of Computational and Applied Mathematics

References in corpus (3)

• Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
• Rigorous numerics for fast-slow systems with one-dimensional slow variable: topological shadowing approach
• On the construction of Lyapunov functions with computer assistance