Aspects of the numerical treatment of higher index DAEs
This chapter sheds light on aspects of the direct numerical treatment of higher index DAEs. Not surprisingly, the integration methods approved for regular index-1 DAEs not longer perform well or fail, if they are applied in the same way to general higher index DAEs. We demonstrate various troubles, e.g., when integrating linear index-3 DAEs. These instabilities and numerical difficulties are due to the ill-posed character of the DAE solutions with respect to perturbations. We do not report index reduction techniques and methods basically exploiting special structural peculiarities to counteract the difficulties, which are discussed by many other authors. We present a procedure for the practical calculation of the index and add a few remarks on consistent initialization in the higher index case. This is of importance for users of DAE solver packages since they usually require knowledge about the DAE index.
KeywordsNumerical Treatment Matrix Sequence Implicit Euler Method Variable Stepsize Tractability Index
Unable to display preview. Download preview PDF.