# Numerical evaluation of systems of ODEs

1. Feb 2, 2012

### SirJac

I'm looking to do numerical evaluation of a system of differential equations and would like to use the RK4 method however I'm having a problem as my differential equations are respect to different variables and I don't know how to adapt RK4 to allow for that. The general form of the equations of motion that I want to evaluate is given below, where $\sigma$ and $\omega$ are functions of both z and t and A,B,C,D and E are all real constants.

$$\frac{\delta \sigma}{\delta t} = iAz \sigma + iB \omega$$
$$\frac{\delta \omega}{\delta z} = -i(C+Dz) \omega + iE \sigma$$

If anyone can't point me in the direction of any resources that consider numerical evaluation of these types of ODE systems, I would greatly appreciate it.