Sobolev gradients for differential algebraic equations

Sobolev gradients and weighted Sobolev gradients have been used for the solution of a variety of ordinary as well as partial differential equations. In the article at hand we apply this method to linear and non-linear ordinary differential algebraic equations and construct suitable gradients for such problems based on a new generic weighting scheme. We explain how they can be put into practice. In the last part, we discuss the performance of our publicly available implementation on some differential algebraic equations and present further applications.