Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations
Author(s)
Sacks, Elisha
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This 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.
Date issued
1988-03-01Other identifiers
AITR-1031
Series/Report no.
AITR-1031
Keywords
qualitative reasoning, dynamic systems, qualitative physics, symbolic mathematics