Application of the combinatorial relaxation algorithm in index reduction method

The mathematical modeling and simulation usually gets a high-index differential-algebraic equation (DAE) system. The structural index reduction algorithms can reduce high-index DAE to low-index DAE. In order to solve the failure of the structural index reduction algorithms in some cases, the authors firstly analyze the combinatorial relaxation algorithm. Then some key algorithms in the implementation of the combinatorial relaxation algorithm are analyzed. Finally, the result of an example shows that the combinatorial relaxation algorithm is an effective way to improve the stability and suitability of the index reduction algorithm based on structural index in DAE.