// Script File: ShowRK
// Plots absolute error for fixed step size Runge-Kutta
// solution to y' = y, y(0) = 1 across [0,5].
// 
for %w=winsid(),xdel(%w);end
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);
     
    //!  mtlb_max(abs(yvals-Exact)) may be replaced by 
    //!     max(abs(yvals-Exact)) if abs(yvals-Exact)is a vector
    //!     max(abs(yvals-Exact),'r') if abs(yvals-Exact)is a matrix
    E(i,k) = mtlb_max(abs(yvals-Exact));
  end
end
mtlb_semilogy([32,64,128,256,512]',E);
xtitle('Runge-Kutta on y''(t) = -y(t), y(0) = 1, 0<=t<=5, h = 5/n',' ',' ');
xtitle(' ','n (Number of Steps)',' ');
xtitle(' ',' ','Maximum absolute error');
xstring(530,E(5,1)+0.003,'k=1');
xstring(530,E(5,2),'k=2');
xstring(530,E(5,3),'k=3');
xstring(530,E(5,4),'k=4');
xstring(530,E(5,5),'k=5');
disp('Evolution des erreurs :')
for i=1:4
  disp(E(i,:) ./ E(i+1, :))
end