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dc.contributor.authorVan Vleck, Erik S.
dc.date.accessioned2015-04-02T16:06:02Z
dc.date.available2015-04-02T16:06:02Z
dc.date.issued2001-03-05
dc.identifier.citationVan Vleck, Erik. "Numerical Shadowing Using Componentwise Bounds and a Sharper Fixed Point Result." (2001) SIAM J. Sci. Comput., 22(3), 787–801. (15 pages). http://dx.doi.org/10.1137/S1064827599353452.en_US
dc.identifier.urihttp://hdl.handle.net/1808/17283
dc.descriptionThis is the published version, also available here: http://dx.doi.org/10.1137/S1064827599353452.en_US
dc.description.abstractShadowing provides a means of obtaining global error bounds for approximate solutions of nonlinear differential equations with interesting dynamics, in particular, for initial value problems with positive Lyapunov exponents. Shadowing breaks down in the presence of zero Lyapunov exponents, although some results such as shadowing with rescaling of time have been obtained. Using a reformulation of the original differential equations and an improved fixed point result we take advantage of componentwise local error bounds to use relatively smaller error tolerances in nonhyperbolic and contractive directions (i.e., in directions corresponding to zero and negative Lyapunov exponents). The result is a decrease in the shadowing global error.en_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.subjectshadowing lemmaen_US
dc.subjecthyperbolicityen_US
dc.subjectglobal error estimationen_US
dc.titleNumerical Shadowing Using Componentwise Bounds and a Sharper Fixed Point Resulten_US
dc.typeArticle
kusw.kuauthorVan Vleck, Erik
kusw.kudepartmentMathematicsen_US
dc.identifier.doi10.1137/S1064827599353452
kusw.oaversionScholarly/refereed, publisher version
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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