Are you using the 3d equivalent of the 2d ADI? If so, then it is unstable. In 2d, the legs are separately unstable but they knock each other out.
The 'fix' is the Peaceman-Rachford method. BTW do you have mixed derivatives like u_xy etc.?
A better approach imo is the Method of Fractional Steps...
I am trying to solve
(1) U_t = 2bU_xy (as part of U_t = aU_xx + 2bU_xy + cU_yy)
using centred finite difference method. When a > 0 everyhing is OK but when a < 0 I get some oscillation problems.
My questions are:
1. is there a pde theory for (1)?
2. what is the 'motivation' for (1)...
What is the precise form of the (linear??) PDE on the right-hand side of?
dF(x,t) / dt = some function of x and F(x,t) ONLY
If there are no spatial derivatives, then it is not a PDE, or am I missing something? Is it not just an ODE system? You also seem to contradict yourself later in your...
For some problems like this one can sometimes use the transformation
z = x + y
w = x - y
Maybe some terms drop off and a new simpler PDE is achieved? It's like a rotation.
Can you provide some more detail? Your question is very general.
For starters, I claim no BC are needed/allowed at x = 0,1.
Sounds like a homework exercise. What is the 'basis' for this PDE?
Another option I am using is to transform the 1/4 plane domain in which Laplace PDE is defined into a unit square, for example using the transformation:
z1 = tanh(x)
z2 = tanh(y)
We then get a convection-diffusion PDE in z1 and z2.
Does anyone know of any sources to this approach...
I wish to approximate the Laplace PDE in a 1/4 plane by truncation of the domain in (x,y) variables:
U_xx + U_yy = 0
Now the PDE is approximated in a box [0, xMax] X [0, yMax] and I can solve it using finite differences.
But the problems are:
1. How to choose xMAx, yMax appropriately...