I am solving a PDE using finite difference which is of the following form:
$F(x,y) =a_{1} F(x+\Delta x,y)+a_{2} F(x-\Delta x,y)+a_{3}F(x,y+\Delta y)+a_{4}F(x,y-\Delta y)$
Where $a_{i}$ are known constants. Furthermore the values of F at the boundaries are known. When I solve this using matlab the solution at one of the boundaries is heavily oscilating. Link to picture. This is the most extreme one, depending on the parameters, the intensity of oscilation varies.
I think this should not be the case but after checking my code multiple times I did not find an error. Has anyone had experience with oscilating solutions at the boundary? Is this something that can happen or can I assume there is an error in the code? Thanks in advance!