Exploiting Fine Block Triangularization and Quasilinearity in   Differential-Algebraic Equation Systems
  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. 
Nedialko S. Nedialkov, Guangning Tan, and John D. Pryce
math.NA