% demo: integrate x'(t) = x(t), x(0)=1
% Stability example, part 2 (unstable method)

 f = inline('x','t','x');

 h  =  input('step size, h: ')
 x = [1; exp(h)];              % begin with exact values for x0, x1

 steps = ceil(1.25/h);
 for k=1:steps-1
    x(k+2) = 3*x(k+1)-2*x(k)+h*(.5*f((k+1)*h,x(k+1)) + (-1.5)*f(k*h,x(k)));
 end

 figure(1), clf
 t = linspace(0,steps*h,500);
 plot(t, exp(t), 'b-', 'linewidth', 2), hold on
 plot([0:h:steps*h], x, 'r-','linewidth',2)
 plot([0:h:steps*h], x, 'r.','markersize',20)
 axis([0 1.25 0 3.5])
 set(gca,'fontsize',16)
 legend('exact', 'method 2',2)