<p> Systems of differential-algebraic equations (DAEs) arise in applications such as circuit
simulation, models of chemical processes, optimal control, and multi-body dynamics. Informally, the index of a DAE is the number of differentiations needed to convert it to an ordinary differential equation. The index generally indicates the difficulty of solving a DAE problem. The higher the index of a DAE, the more difficult it is to solve it numerically.</p> <p> Structural index analysis plays a crucial role in solving DAE problems. In this thesis, we present two methods for index analysis, namely, Pryce's structural analysis (SA) and Linninger's symbolic-numeric (SN) analysis. We provide a Matlab tool implementing these two approaches: an Automatic Structural Index Analyzer (ASIA). We discuss the underlying algorithms, which include generating a signature matrix and computing SA index, computing a system Jacobian, and generating a symbolic-numeric matrix and computing SN index. We also present implementation issues and illustrate how ASIA is used.</p> <p> Numerical experiments show that ASIA can produce reliable structural information. We also show examples on which structural analysis fails, and how ASIA detects such situations.<p> / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/21259 |
| Date | 09 1900 |
| Creators | Liu, Ning |
| Contributors | Nedialkov, Ned, Qiao, Sanzheng, Computing and Software |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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