An asymptotic-numerical approach for examining global solutions to an ordinary differential equation

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dc.creatorRobinson, Michael
dc.date2007-09-28
dc.date.accessioned2026-07-07T08:32:56Z
dc.date.available2026-07-07T08:32:56Z
dc.descriptionPurely numerical methods do not always provide an accurate way to find all the global solutions to nonlinear ODE on infinite intervals. For example, finite-difference methods fail to capture the asymptotic behavior of solutions, which might be critical for ensuring global existence. We first show, by way of a detailed example, how asymptotic information alone provides significant insight into the structure of global solutions to a nonlinear ODE. Then we propose a method for providing this missing asymptotic data to a numerical solver, and show how the combined approach provides more detailed results than either method alone.
dc.description30 pages, 12 figures
dc.identifierhttps://arxiv.org/abs/0709.4664
dc.identifierhttp://arxiv.org/abs/0709.4664
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138957
dc.subjectClassical Analysis and ODEs
dc.subject34E05;34B40
dc.titleAn asymptotic-numerical approach for examining global solutions to an ordinary differential equation
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