TY - JOUR
T1 - An efficient estimate based on FFT in topological verification method
AU - Hiraoka, Yasuaki
AU - Ogawa, Toshiyuki
N1 - Funding Information:
The work of the first author was partially supported by Grant-in-Aid for J.S.P.S. Fellows, 03948.
Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2007/2/15
Y1 - 2007/2/15
N2 - In this paper, localized patterns of the quintic Swift-Hohenberg equation are studied. A numerical verification method with the Conley index theory developed in Zgliczyński and Mischaikow [Rigorous numerics for partial differential equations: the Kuramoto-Sivashinsky equation, Found. Comput. Math. 1 (2001) 255-288] is used in order to prove these patterns. A new technique to efficiently obtain estimates for nonlinear terms is presented. The key idea is based on the pseudo-spectral method. It is shown that this technique is inevitable for the verification of the localized patterns.
AB - In this paper, localized patterns of the quintic Swift-Hohenberg equation are studied. A numerical verification method with the Conley index theory developed in Zgliczyński and Mischaikow [Rigorous numerics for partial differential equations: the Kuramoto-Sivashinsky equation, Found. Comput. Math. 1 (2001) 255-288] is used in order to prove these patterns. A new technique to efficiently obtain estimates for nonlinear terms is presented. The key idea is based on the pseudo-spectral method. It is shown that this technique is inevitable for the verification of the localized patterns.
KW - Conley index
KW - FFT
KW - Numerical verification
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U2 - 10.1016/j.cam.2005.08.036
DO - 10.1016/j.cam.2005.08.036
M3 - Article
AN - SCOPUS:33749674485
SN - 0377-0427
VL - 199
SP - 238
EP - 244
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -