Constraint preserving integrators for general nonlinear higher index DAEs

Abstract

In the last few years there has been considerable research on numerical methods for differential algebraic equations (DAEs) $f(x', x, t) = 0$ where $f_{x'}$ 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 was proposed that could, in principle, be used to integrate general unstructured higher index solvable DAEs. However, that method did not preserve constraints. This paper will discuss a modification of that approach which can be used to design constraint preserving integrators for general nonlinear higher index DAEs.