Embodiments of the present invention simulate a real-world system by first generating a time dependent system of equations that represents the real-world system where the time dependent system of equations has a defined constraint. Next, the constraint is de-coupled from the time-dependent system of equations using a matrix representing an approximation of physics of the real-world system, the de-coupling generating a first system of equations representing the constraint and a second system of equations representing physics of the real-world system. In turn, the generated first and second systems of equations are solved and the real-world system is automatically simulated by generating a simulation using results from solving the first and second systems of equations.