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