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.