R help - Jun 2006 - solving first-order differential equation

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

The fourth-order Runge-Kutta method is in the odesolve package on CRAN, 
but they manual says, only for didactial purposes. First order
differential equations are generally conveniently solved by the 
lsoda function in this package. I hope this helps, even if it does not
directly answer your question.

Best regards,

Johannes Ranke

* ZhanWu Dai <zhanwu.dai at bordeaux.inra.fr> [060612
12:00]:
> 
> 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
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
-- 
Dr. Johannes Ranke                 jranke at uni-bremen.de
UFT Bremen, Leobenerstr. 1         +49 421 218 8971 
D-28359 Bremen                     http://www.uft.uni-bremen.de/chemie/ranke

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
> 
> 
> 
> ------------------------------------------------------------------------
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
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)