how to solve integral in the defining the function command?
1 Ansicht (letzte 30 Tage)
Ältere Kommentare anzeigen
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
is it possible to do this, if yes, how ?
0 Kommentare
Antworten (1)
Torsten
am 19 Jul. 2022
Bearbeitet: Torsten
am 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 Kommentare
Torsten
am 20 Jul. 2022
Bearbeitet: Torsten
am 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Since the equation for y(1) is obsolete, y(2) became y(1) and y(3) became y(2) in the function handle.
Siehe auch
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!