The solution of initial value problems for differential-algebraic equations (DAE)

f(x',x,t) = 0 (1) PP₁(x(t₀),t₀)(x(t₀)-a) = 0 of lower index ( up to 2 ) requires the computation of consistent initial values e.g. to start an integration numerically. Using a suitable index reduction method, the computation of consistent initial values in t₀ leads to the system

f(y₀,x₀,t₀) = 0 (2) PP₁(x₀,t₀)(x₀ - a)+ PQ₁(x₀,t₀)(y₀ +A₂^-1f'_t(y₀,x₀,t₀))+Qy₀ = 0

of nonlinear algebraic equations for determining the unknowns y₀,x₀. For quasilinear DAEs of the form

A(x,t) x' + b(x,t) = 0 we can prove, under mild additional assumptions, that (2) has a nonsingular Jacobian matrix. Examples from electrical network simulation show the applicability of the method.

MINISIMPOSIUM SESSION: 13. Numerical methods for DAEs