[rprenger]

I think what the other commenters are getting at is that PDEs can be used without having a closed form solution (and mostly are used that way as closed form solutions usually only come up in special artificial cases). You start your system in a real known state and then propagate it forward in time using (for example) the finite difference method on the equations to figure out the state at a later time. https://en.wikipedia.org/wiki/Numerical_methods_for_partial_...