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arXiv · 1411.4128

Exploiting Fine Block Triangularization and Quasilinearity in Differential-Algebraic Equation Systems

Nedialko S. Nedialkov·Guangning Tan·John D. Pryce
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Abstract

The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of DAE's system Jacobian is derived; this pattern implies a fine block-triangular form (BTF). This article derives a simple method for quasilinearity analysis of a DAE and combines it with its fine BTF to construct a method for finding the minimal set of initial values needed for consistent initialization and a method for a block-wise computation of derivatives for the solution to the DAE.

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Nedialko S. Nedialkov, Guangning Tan, John D. Pryce. 2014-11-15. Exploiting Fine Block Triangularization and Quasilinearity in Differential-Algebraic Equation Systems. https://arxiv.org/abs/1411.4128

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