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 [itex]\sigma[/itex] and [itex]\omega[/itex] are functions of both z and t and A,B,C,D and E are all real constants.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\delta \sigma}{\delta t} = iAz \sigma + iB \omega [/tex]

[tex]\frac{\delta \omega}{\delta z} = -i(C+Dz) \omega + iE \sigma [/tex]

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.

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# Numerical evaluation of systems of ODEs

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