16.1 Notation

A DAE is defined by a set of expressions for the residuals of differential equations and algebraic equations \(r(y', y, t, \theta)\), and consistent initial conditions \(y(t_0, \theta) = y_0, y'(t_0, \theta)=y'_0\). The DAE is define by residual function as \(r(y', y, t, \theta)=0\). The \(\theta\) dependence is included in the notation to highlight that the solution \(y(t)\) is a function of any parameters used in the computation.