How i can solve two coupled nonlinear first order differential equations

Helo

I want to solve two coupled nonlinear first order differential equations of

dA/dz=-a1*A-1i*w*k*B*(A^*)exp(1i*beta*z)

dB/dz=a2*B-1i*w*(k^*)*(A^2)exp(-1i*beta*z)

where a1,a2,k,w,beta are constant and boundary conditions are A(0)=A0 and B(L)=0

now how i can calculate A(z) and B(z)???

your good help will be highly helpful and appreciable for me

best regards,

[Saman Kohneh Poushi]

Hello Babak

I have a same equation to solve. Please let me know the method of solution if you have gotten that.

Thank you for your help in advance

Best

[Torsten]

Use bvp4c.

[babak janjan]

Hi

you can solve the equation not from z = 0 to z = L, but from z = L to z = 0 and use the well-known Shooting Method.

For more details follow below link

https://link.springer.com/article/10.1007/s10946-012-9273-z

[Nihal Rao]

How did you code the first order ode equation using bvp4c in MATLAB

Answer 1

[Saman Kohneh Poushi]

Dear Torsten and Babak,

Thank you very much for your help. Actually, I'm not expert in coding and I want to solve the following equation.

with these boundary conditions Pe (end) = 0 and Ph (0) = 0.

I wondering to know if there is any solver function to do that.

Best

[Torsten]

As I mentioned: use bvp4c.

But I guess you made an error while specifying your boundary conditions:

If Pe(end) = Ph(0) = 0, then Pe(x) = Ph(x) = 0 for all x.

Answer 2

[Saman Kohneh Poushi]

Thank you again,

The boundary conditions are right. I expect the result would be like this.

[Torsten]

Insert Pe = Ph = 0 for all x in the differential equations and you'll see that they are solutions.