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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