# ode45 or bvp4c? Which one suits this scenario? Please anyone reply

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Jaya il 17 Mag 2021
Modificato: Jaya il 22 Mag 2021
I have a set of differential equations (dPi/dz) for power say for P1 to P7. I have initial power values for P1 to P4 at z=0 and initial power values for P5 to P7 at z= 8. Can I solve this as ode45 or bvp4c?
Because the initial power values I have are not really like boundary conditions. But then how can I use ode45 by using the same P vector definition to have intial values defined for P1 to P4 at one z and for P5 to P7 at another z, as stated above?
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John D'Errico il 22 Mag 2021
Use a boundary value solver, NOT ODE45. However, using a shooting method, as Jan points out, you can use ODE45.
Jaya il 22 Mag 2021
Modificato: Jaya il 22 Mag 2021
OK, thanks. But I hope you have observed the no. of days elapsed between my two questions. I read other stuff too and wanted to ask more specifically since I had implemented and again faced problems. I did not ask repetitively without trying. And I myself wrote why I am asking again in my second question. Thanks.

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### Risposta accettata

Jan il 17 Mag 2021
If some conditions are defined at different time points, the problem is not an "initial value problem", which can be solved by ODE45, but a boundary value problem, for which BVP4C or BVP5C is a suitable solver.
An alternative is to write your own boundary value solver:
Start with a smart guess of the missing components of the initial value and integrate with ODE45. You get a difference between the final values and the boundary values at this time point. Then vary the initial conditions to find out the sensitivity. This can be applied with a Newton method to modify the initial values until the final values are matched. This is the "single shooting method".
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