TY - JOUR
T1 - A numerical verification method for a system of FitzHugh-Nagumo type
AU - Cai, Shuting
AU - Nagatou, Kaori
AU - Watanabe, Yoshitaka
N1 - Funding Information:
The authors would like to express many thanks to referees for their important and useful suggestions to improve this article. This work was supported by PRESTO, Japan Science, and Technology Agency, a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 202244001, No. 21540134).
Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/10/1
Y1 - 2012/10/1
N2 - We propose a numerical method to enclose a solution of the FitzHugh-Nagumo equation with Neumann boundary conditions. We construct, on a computer, a set which satisfies the hypothesis of Schauder's fixed point theorem for a compact map in a certain Sobolev space, which, therefore contains a solution. Several verified results are presented.
AB - We propose a numerical method to enclose a solution of the FitzHugh-Nagumo equation with Neumann boundary conditions. We construct, on a computer, a set which satisfies the hypothesis of Schauder's fixed point theorem for a compact map in a certain Sobolev space, which, therefore contains a solution. Several verified results are presented.
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U2 - 10.1080/01630563.2012.677918
DO - 10.1080/01630563.2012.677918
M3 - Article
AN - SCOPUS:84864699254
VL - 33
SP - 1195
EP - 1220
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
SN - 0163-0563
IS - 10
ER -