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(hold shift key or use mouse wheel to zoom it).
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0 < Xo,Yo < 250.
The script makes 2 it iterations with the time steps
Δt = 0.05 per frame. Set it = 1 and γ = 0
after you get a stationary pattern. Two degenerate eigenmodes
u5,7 and u7,5 are exited.
Set Xo = 100 to see only one mode.
If you are bored of watching relaxation try the
Square wave eigenmodes script.
A CPU based simulation of the wave equation with time periodic perturbation
γ∂t u = Δu + fo
δ(r - ro ) sin ωt,
where γ is small damping (diffusion).
Simple explicit scheme on a 250x250 grid is used. It is stable for
the time steps Δt < h, where h = π/(N-1) is the
space step of the grid.
For the square membrane wave eigenmodes and eigenfrequencies are
un,m = sin(nx) sin(my)
ωo2 = n2 + m2. You can see that in resonance ω = ωo
(and γ = 0) wave amplitude increases to infinity.