Why ode45 is not working?

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Joana Costa
Joana Costa 2020-3-23
回答： Walter Roberson 2020-3-25
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.

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回答（2 个）

Walter Roberson
Walter Roberson 2020-3-25
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.
darova
darova 2020-3-23
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))

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