there is no output, it's keep running but no output, why so?

clc

%defining constant

ti = 0; %inital time

tf = 100E-4;% final time

tspan=[ti tf];

o = 1E6; % detuning frequency

tc = 70E-9; %photon life time in cavity

tf = 240E-6; %flouroscence lifetime

a = 0.02;

P = 1;

k = 0.11; %critical coupling strength

f = @(t,y) [ (2/tc).*((y(3)-a).*y(1) + k.*y(1).*cos(y(3) - pi/2));

(P - y(2).*(y(1)+1)).*(1/tf);

o - 2.*(1/tc).*k.*sin(y(3)-pi/2)

];

[T,Y] = ode45(f,tspan,[1;1;0]);

%plotting the graphs

plot(T,Y(:,3));

%the program is correct i think still it's happening.

Answer 1

[Steven Lord]

Let's look at the value of your integrand at the starting values.

ti = 0; %inital time
tf = 100E-4;% final time
tspan=[ti tf];
o = 1E6;  % detuning frequency
tc = 70E-9;  %photon life time in cavity
tf = 240E-6;  %flouroscence lifetime
a = 0.02;
P = 1;
k = 0.11; %critical coupling strength
f = @(t,y) [ (2/tc).*((y(3)-a).*y(1) + k.*y(1).*cos(y(3) - pi/2));
                       (P - y(2).*(y(1)+1)).*(1/tf);
                      o - 2.*(1/tc).*k.*sin(y(3)-pi/2)
                                       ];
format longg
start = f(ti, [1; 1; 0])

start = 3×1

1.0e+00 * -571428.571428571 -4166.66666666667 4142857.14285714

So two of the three components of the solution plummet while the third takes off like a rocket. If you call ode45 with an OutputFcn you can see that one of the components does take off. If I use OutputSel to select only the second and third components to be plotted, they seem to behave somewhat reasonably, though you will have to stop it due to that first component growing so quickly. I've left the lines below commented out as they wouldn't finish execution before the MATLAB Answers timeout. You can run them in your desktop version of MATLAB.

%{
% Reasonable, 
sol = ode45(f, tspan, [1; 1; 0], odeset('OutputFcn', @odeplot, 'OutputSel', [2 3]));

% Shows the first component taking off
sol = ode45(f, tspan, [1; 1; 0], odeset('OutputFcn', @odeplot, 'OutputSel', 1));
%}

I don't know what that first component of the solution is supposed to represent, but I'm guessing it's not physically realizable. You probably want to check that your implementation matches the equations you're supposed to solve. Those 1/tc and 2/tc look particularly troublesome as tc is 70e-9.