% BCEdemo demonstrates the Backward Cauchy-Euler method
%         for solving the logistic ODE
%         
%         y' = y - y^2,    y(0) = 0.1
%         
%         on the interval [0 100].
%         
% Requires: BkEulerAuto.m, logde.m

close all

tspan = [0 100];
y0 = 0.1;
[t,y] = BkEulerAuto('logde',tspan,y0);
plot(t,y),grid
axis([tspan(1) tspan(2) 0.98 1.02])
xlabel('t'), ylabel('y')
title('Solution of logistic ODE')

h = diff(t);
figure
semilogy(h'), grid
xlabel('Step Number'), ylabel('Step Size')
title('Stepsize history in solution of logistic ODE')