ODEs system

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Andrea 2011-7-26

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https://ww2.mathworks.cn/matlabcentral/answers/12443-odes-system

采纳的回答： Arnaud Miege

i'm trying to solve this system of differential equations, can someone told me how to use the ODE45 function?

dPp/dz= Pp*gammap*(sigmape*N2 −sigmapa*N1)−α*Pp;

dPs/dz= Ps*gammas*(sigmase*N2 −sigmasa*N1)−α*Ps:

dPASE/dz=PASE*gammas*(sigmaSE*N2-sigmasa*N1)+2*sigmase*h*gammas*Vs*Δv-alfas*PASE;

with N1=ρ*(1+W12*t)/(1+(W12+W21)*t+R*t)

N2=ρ*(R*t+W21*t)/(1+(W12+W21)*t+R*t)

W12=[(sigmasa*gammas) / (h*Vs*A)](Ps+PASE) W21=[(sigmase*gammas) / (h*Vs*A)](Ps+PASE) R=[(Pp*gammap*sigmapa) / (h*Vp*A)](Ps+PASE)

(gammap,gammas,sigmase,sigmape,sigmapa,sigmasa,h,Vs,Vp,A,Δv,α,ρ are known parameters).

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Arnaud Miege 2011-7-29

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https://ww2.mathworks.cn/matlabcentral/answers/12443-odes-system#answer_17300

Also, there seems to be 4 variables, not three. Below is the modified code I used and the results I get with your parameters. Again, check the values and the units.

Pp=y(1);
Ps=y(2);
PASE_plus=y(3);
PASE_minus=y(4);
W12=(((sigmasa*gammas)/(h*Vs*A))*(Ps+PASE_plus+PASE_minus));
W21=(((sigmase*gammas)/(h*Vs*A))*(Ps+PASE_plus+PASE_minus));
R=((Pp*gammap*sigmapa)/(h*Vp*A));
N1=(rho*((1+W21*t)/(1+(W12+W21)*t+R*t)));
N2=(rho*((R*t+W12*t)/(1+(W12+W21)*t+R*t)));
dydz(1)=Pp*gammap*(sigmape*N2-sigmapa*N1)-alfap*Pp;
dydz(2)=Ps*gammas*(sigmase*N2-sigmasa*N1)-alfas*Ps;
dydz(3)=PASE_plus*gammas*(sigmase*N2- ... sigmasa*N1)+2*sigmase*N2*gammas*h*Vs*deltav-alfas*PASE_plus;
dydz(4)=-PASE_minus*gammas*(sigmase*N2- ... sigmasa*N1)+2*sigmase*N2*gammas*h*Vs*deltav+alfas*PASE_minus;

And this is how I call the|ode| solver:

[z,y]=ode45('signalFW',[0 20],[10 0.001 0 0]);
figure(1),subplot(2,1,1),plot(z,y(:,1:2)),grid on,ylabel('Power in mW'),legend('Pp','Ps');
subplot(2,1,2),plot(z,y(:,3:4)),grid on,xlabel('length EDFA in m'),ylabel('Power in mW'),legend('PASE+','PASE-');

This gives me the following results:

Is that what you'd expect? If not, check the values of your parameters.

Arnaud

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Andrea 2011-7-29

Your results are the same as mine..maybe there is something wrong with the parameters. Thank you!

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Arnaud Miege 2011-7-27

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https://ww2.mathworks.cn/matlabcentral/answers/12443-odes-system#answer_17088

Have a look at the examples provided in the documentation. You need to write a function that computes the derivatives of your variables as a function of time and the variables themselves, and pass this to the ode solver.

HTH,

Arnaud

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Andrea 2011-7-28

Can I send you an e-mail?

Arnaud Miege 2011-7-29

Can you just upload an image of the equations and the results you expect for certain numerical parameters?

http://www.mathworks.com/matlabcentral/answers/7924-where-can-i-upload-images-and-files-for-use-on-matlab-answers

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Arnaud Miege 2011-7-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/12443-odes-system#answer_17294

This is the results I get with your code:

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Andrea 2011-7-29

You can find the model and the result in these two articles (the correct model is in the second)

http://www.sendspace.com/file/uujskz

http://www.sendspace.com/file/c7abb0

Is my code correct (for the first iteration of the article's model?)

Arnaud Miege 2011-7-29

The code looks correct if you refer to equations (1) to (9) of the paper. However, you should check that the units used for the various parameters are consistent, and that the numerical values make sense.

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