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How can I use FFT to solve this function?

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Yuxing Zhang
Yuxing Zhang 2018-11-25
a.png
My problem is to solve the treamfunction satisfication use FFT method and I do not have ideas how to do it, can anyone help me improve my codes? Or give me some hints please?
tspan=0:0.5:4;
v=0.001;
L=20;n=64;
x2=linspace(-L/2,L/2,n+1);
x=x2(1:n);
y=x;
kx=(2*pi/L)*[0:(n/2-1) (-n/2):-1];
kx(1)=10^-6;
ky=kx;
[X,Y]=meshgrid(x,y);
[KX,KY]=meshgrid(kx,ky);

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