Differential Algebraic Equation - Semi-explicit DAE of Index 1

Semi-explicit DAE of Index 1

DAE of the form

are called semi-explicit. The index-1 property requires that g is solvable for y. In other words, the differentiation index is 1 if by differentiation of the algebraic equations for t an implicit ODE system results,

\begin{align} \dot x&=f(x,y,t)\\ 0&=\partial_x g(x,y,t)\dot x+\partial_y g(x,y,t)\dot y+\partial_t g(x,y,t), \end{align}

which is solvable for if

Every sufficiently smooth DAE is almost everywhere reducible to this semi-explicit index-1 form.

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