Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations
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 sy...
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| Language: | en_US |
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2004
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| Online Access: | http://hdl.handle.net/1721.1/6840 |
| _version_ | 1826194928609263616 |
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| author | Sacks, Elisha |
| author_facet | Sacks, Elisha |
| author_sort | Sacks, Elisha |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T10:04:05Z |
| id | mit-1721.1/6840 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:04:05Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/68402019-04-10T14:25:08Z Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations Sacks, Elisha qualitative reasoning dynamic systems qualitative physics symbolic mathematics 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. 2004-10-20T20:01:04Z 2004-10-20T20:01:04Z 1988-03-01 AITR-1031 http://hdl.handle.net/1721.1/6840 en_US AITR-1031 96 p. 7601294 bytes 5381716 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | qualitative reasoning dynamic systems qualitative physics symbolic mathematics Sacks, Elisha Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations |
| title | Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations |
| title_full | Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations |
| title_fullStr | Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations |
| title_full_unstemmed | Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations |
| title_short | Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations |
| title_sort | automatic qualitative analysis of ordinary differential equations using piecewise linear approximations |
| topic | qualitative reasoning dynamic systems qualitative physics symbolic mathematics |
| url | http://hdl.handle.net/1721.1/6840 |
| work_keys_str_mv | AT sackselisha automaticqualitativeanalysisofordinarydifferentialequationsusingpiecewiselinearapproximations |