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title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Applying methods of the structural analysis of DAE in searching for consistent initial conditions
Creators: name: ÐÐ°Ð½Ð¾Ð²Ð°, ÐÐ»Ð¸Ð·Ð°Ð²ÐµÑÐ°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾-Ð°Ð»Ð³ÐµÐ±ÑÐ°Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ (ÐÐÐ£)
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Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÐÐ°Ð½ÑÐµÐ»Ð¸Ð´Ð¸ÑÐ°
differential-algebraic equations (DAE)
structural analysis
differentiation index
signature method
Pantelides algorithm

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description: The purpose of this work is the implementation of the algorithms for index determining and searching for consistent initial conditions for systems of differential-algebraic equations. Within the work different methods of structural analysis were studied and implemented, as well as basic notions of the subject were discussed including the index concept. The problem of searching for consistent initial conditions requires solving large systems of linear equations so discussion starts with their structural singularity check. In order to simplify numeric solution for nonsingular DAE we use a block lower triangular equations ordering, which based on graph-theoretical Tarjan's algorithm. For higher index DAE we use additional analysis with Pantelides algorithm and Signature method to find hidden constraints. This methods gives the same results applied for the first order DAE, but each of them have its own features, described in this paper. Considered algorithms were implemented, tested and applied for several hydraulic problems. As a result of their structural analysis, models indexes were determined and equations necessary for finding consistent initial conditions were obtained.