[R] Solution to differential equation

[dave fournier]

Ravi Varadhan wrote:

Because the numerical solution is more flexible. In the example I linked 
to the
population is being fished. This add an extra term which breaks your 
solution.
I don't know where the OP is going with this question, but flexibility 
might be
useful. Also I just like the idea of fitting models defined by DE's to 
data.

> When you can obtain `exact' (but not closed-form) solution, why would you
> want to use a numerical ODE solver, which has an approximation error of the
> order O(dt) or O(dt^2), where `dt' is the time step? Furthermore, a
> significant advantage of an exact solution is that you can compute the
> solution at any given `t' in one shot, rather than having to march through
> time from t=t0 to t=t.  Numerical time-marching schemes make more sense for
> systems of nonlinear ODEs.
>
> Ravi.
>
> -------------------------------------------------------
> Ravi Varadhan, Ph.D.
> Assistant Professor,
> Division of Geriatric Medicine and Gerontology School of Medicine Johns
> Hopkins University
>
> Ph. (410) 502-2619
> email: rvaradhan at jhmi.edu
>
>
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
> Behalf Of dave fournier
> Sent: Friday, December 17, 2010 11:23 AM
> To: r-help at r-project.org
> Subject: Re: [R] Solution to differential equation
>
>
> It is not very difficult to integrate this DE numerically.
> For parameter estimation it is a good idea for
> stability to use a semi-implicit formulation. The idea is
> described here.
>
>      http://otter-rsch.com/admodel/cc4.html
>
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