The idea is that you use numerical methods to solve those equations. I suggest you look into Finite difference method. It is the easiest methods that i have seen, but coding these algorithms are no easy task. You can look for some codes that are readily available, but I am not sure where to find them. I am currently working on my own code, in matlab, to solve Maxwell equations using the finite difference method. Another option is to use an EM solver that already exists e.g. HFSS, COMSOL, FEKO. I use HFSS a lot!