Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations
Abstract
This thesis explores automating the qualitative analysis of physical systems. Scientists and engineers model many physical systems with ordinary differential equations. They deduce the behavior of the systems by analyzing the equations. Most realistic models are nonlinear, hence difficult or impossible to solve explicitly. Analysts must resort to approximations or to sophisticated mathematical techniques. The author describes a computer program, called PLR (for Piecewise Linear Reasoner), that formalizes an analysis strategy employed by experts. PLR takes parametrized ordinary differential equations as input and produces a qualitative description of the solution for all initial values. It 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1988
- Accession Number
- ADA196310
Entities
People
- Elisha P. Sacks
Organizations
- Massachusetts Institute of Technology