Can Runge-Kutta be used for problems with more than 2 independent variables?

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SUMMARY

The Runge-Kutta method is applicable only for problems with a single independent variable, specifically time (t). In the discussed scenario, the equation dy/dt = f(u, v, r) requires that all variables (u, v, r, L) be expressed as functions of t for the method to be valid. The necessity of uncoupling r and L is highlighted, as L can potentially be expressed in terms of u and v, complicating the implementation. Therefore, for successful application of Runge-Kutta, all variables must be appropriately defined in relation to the independent variable.

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hoomanya
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Hi,

I am trying to use the Runge-Kutta method for a problem that looks like this:

dy/dt= f(u,v,r)
where y= r*L


I was wondering if dy/dt can be a function of more than 2 independent variables?

Also do I need to do some kind of uncoupling of r and L? (I think L can be in a way expressed in terms of u and v but that would make things even more complicated I guess. )

Thanks,

H
 
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Runge-Kutta works for only 1 independent variable, i.e t in this problem. Ultimately, u, v, r, L must all be expressed as functions of t for Runge-Kutta to work.
 

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