Computational speedup for general nonlinear higher index DAE integrators

There has been considerable research on numerical methods for differential algebraic equations (DAEs) f(x ′,x,t) = 0 where fx ′ is identically singular.The index provides one measure of the singularity of a DAE.Most of the numerical analysis literature on DAEs to date has dealt with DAEs with indices no larger than three.Even in this case, the systems were often assumed to have a special structure.Recently a numerical method has been proposed that can, in principle, be used to integrate general unstructured higher index solvable DAEs.Modifications of this approach can be used to design constraint preserving integrators for general nonlinear higher index DAEs.Previous work on these more general approaches has focused on their feasibility and theoretical basis.This paper examines some of the issues involved with their computationally efficient implementation