Solving more general index-2 differential algebraic equations

Abstract The paper deals with a class of quasilinear index-2 differential algebraic equations, which covers both linear variable coefficient systems as well as Hessenberg form equations. Supposing low smoothness only, the solvability of initial value problems is stated via classical analytical techniques. For that class of differential algebraic equations, backward differentiation formulas and Runge-Kutta methods as well as projected versions are discussed with respect to feasibility, (in)stability, convergence, and asymptotical behaviour.