This paper introduces the implicit-IMOR method for differential algebraic equations. This method is a modification of the Index-aware model order reduction (IMOR) method proposed in our earlier papers which is the explicit-IMOR method. It also involves first splitting the differential-algebraic equations (DAEs) into differential and algebraic parts using a basis of projectors. In contrast with the explicit-IMOR method, the implicit-IMOR method leads to implicit differential and algebraic parts. We demonstrate the implicit-IMOR method using the RLC/RC networks, but it can also be applied to other problems which lead to differential-algebraic equations.
Banagaaya, N., Ali, G., Schilders, W. H. A., & Tischendorf, C. (2014). Implicit index-aware model order reduction for RLC/RC networks. In Design, Automation and Test in Europe (DATE 2014, Dresden, Germany, March 24-28, 2014) (pp. 1-6). EDAA. https://doi.org/10.7873/DATE2014.056