1. A computer-implemented method for identifying errors in a system model, the method comprising: identifying at least one matrix corresponding to a plurality of numerical equations, a numerical equation corresponding to at least one of a component of the system model and a topology equation of the system model; performing, using a processor, a numerical analysis of the identified at least one matrix to identify at least one illegal configuration in the system model, the numerical analysis comprising: identifying a first numerical equation from the plurality of numerical equations, identifying a second numerical equation from the plurality of numerical equations, and operating on the matrix to identify the illegal configuration, the illegal configuration being identified if it is determined that a dependency exists between the first numerical equation and the second numerical equation; and providing an indication of the identified at least one illegal configuration of the system model.