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On Estimation of the Global Error of Numerical Solution on Canard-Cycles Full article

Общее Language: Английский, Genre: Full article,
Status: Published, Source type: Original
Journal Mathematics and Computers in Simulation
ISSN: 0378-4754 , E-ISSN: 1872-7166
Output data Year: 2015, Volume: 116, Pages: 59-74 Pages count : 16 DOI: 10.1016/j.matcom.2014.10.003
Tags Canards, Chemical kinetics, Global error of numerical integration, Nonlinear dynamical system
Authors Chumakov G.A. 1,3 , Lashina E.A. 2,3 , Chumakova N.A. 2,3
Affiliations
1 Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk 630090, Russia
2 Boreskov Institute of Catalysis, pr. Akad. Lavrent’eva 5, Novosibirsk 630090, Russia
3 Novosibirsk State University, ul. Pirogova 2, Novosibirsk 630090, Russia

Funding (1)

1 Президиум СО РАН 80

Abstract: Under study is the behavior of the global error of numerical integration in the two-variable mathematical model of a heterogeneous catalytic reaction. Numerical estimation of the global error indicates that there is a high sensitive dependence of the solutions on initial conditions due to the existence of a tunnel-type bundle of trajectories which is formed by the stable and unstable canards. We show that the exponential growth of the norm of the fundamental matrix of solutions of the system linearized around a stable canard-cycle yields exponential growth of the leading term in the global error of numerical solution
Cite: Chumakov G.A. , Lashina E.A. , Chumakova N.A.
On Estimation of the Global Error of Numerical Solution on Canard-Cycles
Mathematics and Computers in Simulation. 2015. V.116. P.59-74. DOI: 10.1016/j.matcom.2014.10.003 publication_identifier_short.wos_identifier_type publication_identifier_short.scopus_identifier_type publication_identifier_short.rinz_identifier_type
Dates:
Submitted: Jun 27, 2014
Accepted: Oct 13, 2014
Published online: Oct 22, 2014
Published print: Oct 1, 2015
Identifiers:
publication_identifier.wos_identifier_type WOS:000357240400004
publication_identifier.scopus_identifier_type 2-s2.0-84930865063
publication_identifier.rinz_identifier_type 23970820
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