Once a model has been developed it must be solved in some way to produce the required process dynamic responses. There are two ways of going about this: numerical solutions, where the solution is approximated by some numerical integration algorithm; and analytical solutions where the differential equations are solved symbolically. Numerical solution is by far the most common technique when dynamic simulation is the goal. This is because numerical simulation is far more flexible, can handle non-linearities in the equations, and can be linked directly to physical property databases. An analytical solution usually requires that models be simplified prior to solution, and in particular non-linear equations have to be linearised. While this is an unnecessary hassle for purely modelling purposes, analytical solutions are useful for control system design. It is therefore necessary for you to have an understanding of both techniques.