Why ode45 is not working?

Hello, I am trying to solve the following equations using ode45:

function dydt = odefun3(t,y)
dydt = zeros(3,1);
dydt(1) = 4.86*y(3) - 4.86*10^14*y(1)*y(2);
dydt(2) = 4.86*y(3) - 4.86*10^14*y(1)*y(2);
dydt(3) = -4.86*y(3) + 4.86*10^14*y(1)*y(2);
 
tspan = [0 0.05 0.5 1 4];
y0 = [1.48*10^-8; 6.7608*10^-3; 1];  
[t,y] = ode45(@(t,y) odefun3(t,y),tspan,y0);

I am having problems because I am not getting results, it takes too long. I am thinking it can be a time step problem because if I use a smaller tspan = [0 1*10^-10] I can get results however I will need results accordingly to tspan = [0 0.05 0.5 1 4].

Have you got any idea about this? Thank you for your help.

[Walter Roberson]

I suspect that you need a stiff solver such as ode23s

Answer 1

[Walter Roberson]

Your function wiggles a lot, with the first derivative crossing and recrossing 0. ode45s needs to take very small steps in order to model the behaviour properly.

If you change from ode45 to ode23s then it will finish quickly, at the expensive of not being completely accurate at the fine detail.

Answer 2

[darova]

I changed tspan

f = @(t,y) [ 4.86*y(3) - 4.86*10^14*y(1)*y(2);
             4.86*y(3) - 4.86*10^14*y(1)*y(2);
            -4.86*y(3) + 4.86*10^14*y(1)*y(2) ];
opt = odeset('maxstep',1e-13);
tspan = [0 1e-11];
y0 = [1.48e-8; 6.7608e-3; 1];  
[t,y] = ode45(f,tspan,y0,opt);
subplot(311)
plot(t,y(:,1))
subplot(312)
plot(t,y(:,2))
subplot(313)
plot(t,y(:,3))