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Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations

dc.date.accessioned2004-10-20T20:01:04Z
dc.date.accessioned2018-11-24T10:22:05Z
dc.date.available2004-10-20T20:01:04Z
dc.date.available2018-11-24T10:22:05Z
dc.date.issued1988-03-01en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/6840
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/1721.1/6840
dc.description.abstractThis paper explores automating the qualitative analysis of physical systems. It describes a program, called PLR, that takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values. PLR approximates intractable nonlinear systems with piecewise linear ones, analyzes the approximations, and draws conclusions about the original systems. It chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes, yet simple enough to be analyzed completely and efficiently. It derives additional properties, such as boundedness or periodicity, by theoretical methods. I demonstrate PLR on several common nonlinear systems and on published examples from mechanical engineering.en_US
dc.format.extent96 p.en_US
dc.format.extent7601294 bytes
dc.format.extent5381716 bytes
dc.language.isoen_US
dc.subjectqualitative reasoningen_US
dc.subjectdynamic systemsen_US
dc.subjectqualitative physicsen_US
dc.subjectsymbolic mathematicsen_US
dc.titleAutomatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximationsen_US


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