Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations

Title: en_US Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations
Creator: en_US Sacks, Elisha
Date: 2004-10-20T20:01:04Z
Date Available: 2004-10-20T20:01:04Z
Date Issued: en_US 1988-03-01
Identifier: en_US AITR-1031
uri: http://hdl.handle.net/1721.1/6840
Abstract: en_US 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.
Extent: en_US 96 p.; 7601294 bytes; 5381716 bytes
Format: application/postscript; application/pdf
Language: en_US
Relation: en_US AITR-1031
Subject: en_US qualitative reasoning; en_US dynamic systems; en_US qualitative physics; en_US symbolic mathematics