I am intending to use Runge Kutta 4th order to numerically solve a system of coupled equations:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{d^{2}x}{dt^{2}}[/itex] = K_{1}* x * cos(t) + ( (K_{2}* [itex]\frac{dy}{dt}[/itex]) - [itex]\frac{dz}{dt}[/itex] )

[itex]\frac{d^{2}y}{dt^{2}}[/itex]= -K_{1}* y * cos(t) + ( (K_{2}* [itex]\frac{dz}{dt}[/itex]) - [itex]\frac{dx}{dt}[/itex] )

[itex]\frac{d^{2}z}{dt^{2}}[/itex]= ( (K_{2}* [itex]\frac{dx}{dt}[/itex]) - [itex]\frac{dy}{dt}[/itex] )

I'm really a bit stuck to be honest. I've only ever used RK4 on 1st order linear ODEs. I've been reading around alot but not making much progress.

Initial values for [itex]\frac{dx}{dt}[/itex], [itex]\frac{dy}{dt}[/itex], [itex]\frac{dz}{dt}[/itex] are all known. The constants K are known.

Can anyone please help? Thanks

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# Numerical Integration of 2nd Order DE

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