Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shin'ichi Oishi
Published 2016-06-09Version 1
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.
Comments: 29 pages, 7 figures, 2 tables
Numerical validation of blow-up solutions with quasi-homogeneous compactifications
Invariant Variational Schemes for Ordinary Differential Equations
Performance Evaluation of an Extrapolation Method for Ordinary Differential Equations with Error-free Transformation
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