# Question:Solving ODE - shooting method, Runge-Kutta method of 4th order

## Question:Solving ODE - shooting method, Runge-Kutta method of 4th order

Maple

Hi guys,

I have got serious problem with solving this system of ODE, where psi is equal to 10*sqrt(da) and uB,E,kL,uc are constants:

firstly I have to find missing initial condition using shooting method and calculate cA(z=2) using Runge-Kutta 4th order then. And plot following concentration profile for cA and dA. So far, I have dealt with first diff eq 2nd order dividing by two diff eq of 1st order using mentioned constants so I got these ones:

dy[1]:=y2(z);
dy[2]:=1.000000000*sqrt(y1(z))-6.000000000*y2(z)-10.00000000*y3(z);
dy[3]:=-0.8333333333e-2*sqrt(y1(z))-0.8333333333e-1*y3(z);

I understand I need a condition da(z=0) that I should obtain using shooting method, but I do not know how to do it in spite of I understand it in theoretical way. And same problem I have with RK4th order. Anybody here with a hint, please?

There is my maple file (unfinished version of mine): maple-shoot_RK4.mw

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