Undergrad Rosenbrock method ODE : Abrupt increase during First iteration

[gurbir_s]

TL;DR

I am using Rosenbrock4 method from Odeint library in C++ to solve a set of differential equations. However, I see that it gives an unusual change in the result for first iteration but afterwards, gives good results. How can I solve it?

The set of equations is

I have first tried to solve only first two equations (removing the components of other 4 equations from them.)

This is the output, where first column is the time, 2nd - X_p, and 3rd - X_n

 

[berkeman]

How are you setting your initial conditions for this solution?

 

[gurbir_s]

How are you setting your initial conditions for this solution?

The $X_i$'s are elemental abundances during Big Bang Nucleosynthesis. I set the initial conditions equal to their thermal equilibrium values at that point.

I don't know how, but the problem got solved automatically while I was trying to solve another problem. Idk how. Thanks for your reply.