Journal Article Numerical validation of blow-up solutions of ordinary differential equations

Takayasu, Akitoshi  ,  Matsue, Kaname  ,  Sasaki, Takiko  ,  Tanaka, Kazuaki  ,  Mizuguchi, Makoto  ,  Oishi, Shin’ichi

314pp.10 - 29 , 2017-04 , Elsevier
ISSN:0377-0427
NCID:AA00696002
Description
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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