In simulating a physical circuit or system including analog and mixed signal digital-analog components, a physical circuit or system includes components defined as instances of models. There can be multiple instances of any model in the physical circuit or system. For each model, a sub-system of simultaneous equations is determined. The variables in the sub-systems of simultaneous equations are classified as input, output, intermediate, or system variables. Equations are associated with each variable, and the sub-systems of simultaneous equations are reduced by eliminating all equations not associated with system variables. The system of simultaneous equations describing the physical circuit or system is assembled from the sub-systems of simultaneous equations. For each instance of a model, a copy of the sub-system of simultaneous equations for that model is added to the system of simultaneous equations. The system of simultaneous equations can then be solved, and the results used to analyze the behavior of the physical circuit or system.