You are missing the distinction between a numerical solution to a set of equations and an analytical one. Usually, the analytical solution gives you the dynamic

You are missing the distinction between a numerical solution to a set of equations and an analytical one. Usually, the analytical solution gives you the dynamics of a system at any point in time and space given a set of parameters. For numerical solutions you have to run each individual set of parameters to find the corresponding values in time and space (not even considering stochastic equations). This is very computationally expensive. This is the value in solving these things analytical — hence the prize.