% ShowRK2 script demonstrates
% error of 2nd-order Runge-Kutta method
% Requires RK2FixH, lnhde

close all
colors='ymcrgb';
xspan=[0 2*pi];y0=0;
figure(1)
hold on

for p = 6:9
  nsteps = 2^p;
  [x,y]=RK2FixH('lnhde',xspan,y0,nsteps);
  yext = (25/13)*cos(x) + ...
          (5/13)*sin(x) - ...
         (25/13)*exp(-5*x);
  err=(y-yext);
  plot(x,err,colors(p-3))
end
xlabel('x')
ylabel('y_{Computed} - y_{Exact}')
title('Error in Runke-Kutta-2 solution with 2^{6}, 2^{7}, 2^{8}, 2^{9} steps')