I posted the question below in
Stackoverflow but then realized that it perhaps would find a better audience here.
I am solving a fourth order non-linear partial differential equation
in time and space
(t, x) on a square domain with periodic or free
boundary conditions with MATHEMATICA.
Without using conformal mapping, what boundary conditions at the edge or corner could I use to make the square domain "seem" like a circular domain for my non-linear partial differential equation which is cartesian?
The options I would not like to use are:
- Conformal mapping
- changing my equation to polar/cylindrical coordinates?
This is something I am pursuing purely out of interest just in case
someone screams bloody murder if misconstrued as a homework problem!
If I have a result from solving a PDE in cartesian coordinates, how do I transfer these results or view them in polar coordinates?