Order of Magnitude Reasoning in Qualitative Differential Equations

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment over orders of magnitude, including a complete categorization of adjacent pairs of qualitative states. We show how this theory can be applied to simple problems, we give an algorithm for generating a complete envisionment graph, and we discuss the implementation of this algorithm in a running program.

Original languageEnglish (US)
Title of host publicationReadings in Qualitative Reasoning About Physical Systems
PublisherElsevier Inc.
Pages422-434
Number of pages13
ISBN (Print)1558600957, 9781483214474
DOIs
StatePublished - Sep 17 2013

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Differential equations
Dynamical systems

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Davis, E. (2013). Order of Magnitude Reasoning in Qualitative Differential Equations. In Readings in Qualitative Reasoning About Physical Systems (pp. 422-434). Elsevier Inc.. https://doi.org/10.1016/B978-1-4832-1447-4.50039-0

Order of Magnitude Reasoning in Qualitative Differential Equations. / Davis, Ernest.

Readings in Qualitative Reasoning About Physical Systems. Elsevier Inc., 2013. p. 422-434.

Research output: Chapter in Book/Report/Conference proceedingChapter

Davis, E 2013, Order of Magnitude Reasoning in Qualitative Differential Equations. in Readings in Qualitative Reasoning About Physical Systems. Elsevier Inc., pp. 422-434. https://doi.org/10.1016/B978-1-4832-1447-4.50039-0
Davis E. Order of Magnitude Reasoning in Qualitative Differential Equations. In Readings in Qualitative Reasoning About Physical Systems. Elsevier Inc. 2013. p. 422-434 https://doi.org/10.1016/B978-1-4832-1447-4.50039-0
Davis, Ernest. / Order of Magnitude Reasoning in Qualitative Differential Equations. Readings in Qualitative Reasoning About Physical Systems. Elsevier Inc., 2013. pp. 422-434
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