In industry, the “model-based development (MBD)” is becoming very important. The MBD is as follows. In the development of a machine or a plant, its theoretical model is given first, where the model is a system of differential-algebraic equations (DAEs) with quite many parameters in coefficients, and the model is tested by numerical simulation to determine optimal parameter values [1]. One important feature of the model is that each equation contains several terms mostly, hence the resulting linear system is very sparse. The DAEs are very ill-conditioned to solve numerically, so it is usually converted into a system of ordinary differential equations; we do not enter into the conversion in this poster.
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