I have a system of coupled ODEs which tells the propagation of power P(adsbygoogle = window.adsbygoogle || []).push({}); _{i}in an optic fiber.

[tex]

\frac{\partial P_i }{\partial z} = \left (N\sigma - 1 \right ) P_i

[/tex]

where

[tex] N = \frac{\sum_i \alpha_i P_i}{\sum_i \beta_i P_i + 1}

[/tex]

If the signals are copropagating, there is no problem since it is easily solvable with ode45 in MATLAB. However, since there are signals which are propagating in the opposite direction, solutions must be relaxed (according to the Book) so that the forward and backward propagation powers would agree.

I'm solving the system from z = [0,L]. For those forward propagating signals, P_i(0)=finite. For those backward propagating signals, P_i(L) = some value. Can I solve this using initial value problem techniques in MATLAB? or do i need to move to boundary-value problem techniques. The thing is, I only know one side of the boundary, the value on the other side is my objective.

Please help. :)

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# MATLAB solution to system of ODEs with forward and backward propagation

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