how to solve integral in the defining the function command?
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clc
%defining constant
ti = 0; %inital time
tf = 10E-5;% final time
tspan=[ti tf];
o = 10E6; % detuning frequency
tc = 70E-9; %photon life time in cavity
tf = 240E-6; %flouroscence lifetime
a = 0.02; %round trip loss
P = 1; %pump strenght
k = 0.2; %critical coupling strength
l= 0.5;
% define function
%y(1) = I
%y(2) = G
%y(3) = phase difference
f = @(t,y) [
((y(2)-a-l.*(abs(cos(y(3)+ pi/4)))).*y(1) + k.*y(1).*cos(y(3)- pi/2)).*(2/tc);
(P - (y(2).*(y(1) + 1))) / tf;
o - (k / tc).*2.* sin(y(3));
];
%initial consitions
[T,Y] = ode45(f,tspan,[1;1;1]*10E-5);
%plotting the graphs
plot(T,Y(:,3));
ylim([0 30])
in this the program I represent y(1) as I(Φ), in the equation 2 intead of y(1) i want to use integral of I(Φ)dΦ , where the we assume I(Φ) is gaussian distribution with a variable mean Φ0 and constant rms width σ = 0.1
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1070315/image.png)
is it possible to do this, if yes, how ?
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Answers (1)
Torsten
on 19 Jul 2022
Edited: Torsten
on 19 Jul 2022
integral_{0}^(t) I(phi) dphi = normcdf(t,0,0.1) - 0.5
So you can work with
y(1) = normcdf(t,0,0.1) - 0.5
in your equations.
2 Comments
Torsten
on 20 Jul 2022
Edited: Torsten
on 20 Jul 2022
I don't know the background of your equations.
If you want to take y1 as integral of I(Φ)dΦ , where we assume I(Φ) is gaussian distribution with a variable mean Φ0 and constant rms width σ = 0.1, the equations are
f = @(t,y) [ (P - (y(1).*(normcdf(t,0,0.1) - 0.5 + 1))) / tf; o - (k / tc).*2.* sin(y(2)) ];
Since the equation for y(1) is obsolete, y(2) became y(1) and y(3) became y(2) in the function handle.
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