% Theodorsen data for inverted ellipse
% error with exact map f(z) compared with CR^(N/2) with N Fourier points
err8=[8.3*10^(-4) 6.1*10^(-6) 5.1*10^(-10) 5.6*10^(-16)]; % errors with alpha=.8
R=3; %R=sqrt{(1+alpha)/(1-alpha)} from my 1994 paper
C8=err8(1)/(R^(-4));
R8dat=C8*[R^(-4) R^(-8) R^(-16) R^(-32)]; 
Naxis8=[8 16 32 64];
err6=[8.6*10^(-3) 3.0*10^(-4) 6.7*10^(-7) 5.5*10^(-12) 5.6*10^(-16)]; % errors with alpha=.6
R=2;
C6=err6(1)/(R^(-4));
R6dat=C6*[R^(-4) R^(-8) R^(-16) R^(-32) R^(-64)]; 
Naxis6=[8 16 32 64 128];
semilogy(Naxis8,err8,'o',Naxis8,R8dat,'--',Naxis6,err6,'x',Naxis6,R6dat,'--');
xlabel('N')
ylabel('error = ||f(z)-f_N(z)||_{\infty}') 