# Some question about a special code for solving an ODE system by Runge-Kutta method

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Mojtaba Mohareri on 20 Jan 2020
Commented: Mojtaba Mohareri on 21 Jan 2020
The solution of my problem consists of two parts:
First, I want to solve the follwong system
by Runge-Kutta fourth order method and obtain the values of (C,R,P), where N=C+R+P, lambda and alpha values are known, gamma and beta functions are given and u1(t) and u2(t) are as follows
where k2 and k3 are known.
Next using those values, I solve the following system
again by Runge-Kutta fourth order method and obtain the values of (p1,p2,p3).
My problem is that I don't know how to solve C, R and P in terms of p1, p2 and p3 (in the first system) by Runge-Kutta method for substituting in the next system. I can just solve the first system when u1(t) and u2(t) are constants. I was wnodering if you could help me about my problem. Thank you in advance.

Bjorn Gustavsson on 20 Jan 2020
Since u1 and u2 depends on p1, p2 and p3, that in turn will depend on time, you have 6 coupled ODEs. The best(?) way to solve these is to do it simultaneously, that is write yourself a function something like this:
function dRCPp1p2p3dt = ode4RCPp1p2p3(t,RCPp1p2p3,alpha1,kappa2)
dRCPp1p2p3dt = zeros(6,1);
dRCPp1p2p3dt(1) = -lambda2* ...etc, for your equation of R-dot
dRCPp1p2p3dt(2) = -lambda1* ...etc, for your equation of C-dot
% and so on, you should be able to calculate your derivatives of all your function here
end
You obviosly also have to make sure that the other time-dependent functions are callable. Then it should just be to integrate this with the standard ODE-functions for the initial conditions of interest.
HTH.

#### 1 Comment

Mojtaba Mohareri on 21 Jan 2020
Thank you very much for your help. It works properly.