mode(-1);
// Script File: ShowRK
// 
// Plots absolute error for fixed step size Runge-Kutta
// solution to y' = y, y(0) = 1 across [0,5].

getf('Ordre.sci');
getf('funcs.sci');

xbasc();
E = zeros(5,5);
for i = 1:5
  n = 16*(2^i);
  Exact = exp(-linspace(0,5,n+1));
  for k = 1:5
    [tvals,yvals] = FixedRK(f1,0,1,5/n,k,n);
    E(i,k) = max(abs(yvals-Exact));
  end
end
//%   semilogy([32 64 128 256 512]',E)
xset("font",2, 3);
plot2d('ll',(5)./[32,64,128,256,512]',E ,style=(1:5),strf='121',leg='k=1@k=2@k=3@k=4@k=5') 
plot2d('ll',(5)./[32,64,128,256,512]',E ,style=-(1:5)) 
xtitle('Runge-Kutta on y''(t) = -y(t), y(0) = 1, 0<=t<=5, h = 5/n','5/n','Erreur max.');

// pentes=-log10(E(5,:))+log10(E(1,:));
// printf("Ordre    pente\n")
// for k=1:5
//   printf("%g      %g\n", k, pentes(k))
// end