Detecting and Correcting the Index of DAE by the Combinatorial Relaxation Algorithm

The mathematical modeling and simulation based on the Modelica language usually gets a high-index differential-algebraic equation (DAE) system. The structural index reduction algorithms can serve as a fast method to reduce such high-indexed issues. In order to solve the failure of the structural index reduction algorithms in some cases, the combinatorial relaxation algorithm is analyzed and studied. Finally, the result of an example shows the combinatorial relaxation algorithm is an effective way to improve the stability of the index reduction algorithms based on the structural index of DAE.