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: rvarad...@jhmi.edu -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of dave fournier Sent: Friday, December 17, 2010 11:23 AM To: r-help@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 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.