# Re: [R] solving first-order differential equation

From: Joerg van den Hoff <j.van_den_hoff_at_fz-rossendorf.de>
Date: Mon 12 Jun 2006 - 21:59:20 EST

ZhanWu Dai wrote:
> I am an initial user of R. Could you give me some explanations or examples on how to solve the first order differential equations by the first-order Runge-Kutta method?
>
> Thank you very much
>
> Kind regards
>
>
>
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not really an answer, but a remark:

if your ODE is of the form

dy
--- - k y = A f(x)
dx

(k, A const.) it might be a better idea to use the 'analytic' solution instead of runge-kutta (faster, probably more accurate). for instance, if the initial condition is

y(x=0) = 0

and you're looking only at x>0 the solution simply is

y(x) = A (x) {*} exp(-kx)

where {*} means the finite (continous) convolution extending from 0 to x:

y(x) = A integral from z=0 to z=x {f(z) exp(-k(x-z)) dz}

(which, of course, still has to be computed numerically in general.) this closed-form solution can then
be used, for instance, to determine the unknown parameters (k, A) from a least squares fit to measured f(x), y(x)

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