[rahimiali]

Runge-kutta works when you’re given an initial condition and the derivative is with respect to just one variable (so you’re given f(t) just at t=0). What do you do when you’re given a boundary condition and the derivative is with respect to many variables? This.

[the_svd_doctor]

I mean, you can also just do finite differences. Of course Galerkin opens up the very “rich” design space of finite elements methods.

[bunje]

Finite differences are simple in cubes and domains that can be mapped to one. Not so much in an arbitrary tetrahedral mesh.