clear
format compact

%%
f = @(t,u) sin( (t+u).^2 );
[t, u] = ode45(f, [0,4], -1);

plot(t, u)
xlabel('t')
ylabel('u(t)')
title('Solution of du/dt=sin[(u+t)^2]')
grid on
%%
% We return to the equation u'=sin[(u+t)^2] to see two variations on how 
% to obtain numerical solutions for it. In the first one, we
% can supply a vector of time nodes and receive the solution at exactly
% those times. 
t = linspace(0, 4, 60)';
[t, u] = ode45(f, t, -1);

plot(t, u, '.')
xlabel('t')
ylabel('u(t)')
title('Solution at 60 points')
grid on

%% 
% In the second variation, we see that it's also possible to create a 
% callable function for the solution. Essentially this is a high-quality 
% interpolant of the computed particular values. 
u = @(t) deval( ode45(f, [0,4], -1), t );
fplot(u, [0,4])
xlabel('t')
ylabel('u(t)')
title('Solution as a callable function')
grid on