@article{9e9a73c167814420b53815183132a0ca,
title = "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.",
keywords = "Blow-up solutions, Compactifications, Lyapunov functions, Ordinary differential equations, Validated computations",
author = "Akitoshi Takayasu and Kaname Matsue and Takiko Sasaki and Kazuaki Tanaka and Makoto Mizuguchi and Shin'ichi Oishi",
note = "Funding Information: AT was partially supported by JSPS Grant-in-Aid for Young Scientists (B), No. 15K17596 . KM was partially supported by The Coop with Math Program, a commissioned project by Ministry of Education, Culture, Sports, Science and Technology (MEXT) . SO was partially supported by CREST, JST . The authors also wish to thank Prof. Nobito Yamamoto, who provided them with the essential suggestion of re-parameterization in the integrals of ODEs via Lyapunov functions. Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",
year = "2017",
month = apr,
day = "1",
doi = "10.1016/j.cam.2016.10.013",
language = "English",
volume = "314",
pages = "10--29",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",
}