From: Didier Pieroux Subject: Re: Solution for linear ''retarded'' DE Date: Tue, 04 Jan 2000 12:56:31 +0100 Newsgroups: sci.math.num-analysis Summary: [missing] Hi Thomas, > I'm in need of a FORTRAN-routine which solves the following > linear ''retarded'' DE: > mx�� + dx� + cx = const[x(t-t*)-x(t)] I greatly recommend you: Hairer, Norsett and Wanner, Solving Ordinary Differential Equations, Tome I, Nonstiff Problems Springer-Verlag ISBN: 3-540-56670-8, and especially sections II 6: Dense output II 17: Delay differential Equations. In addition, the subroutine "Retard" (in the Appendix of the book) should suit your needs. Otherwise, as your problem looks not that hard, you can use a constant step size method (RK4 for example) and choose the time step size to be dt=t*/N, where N is an integer. This is for sure the easiest method to implement from scratch ! If you want a variable step size method, you can use a RK4(3) method and interpolate the value of x(t-t*) by using Hermite interpolation on the previously computed points. Be careful then that your time step be always greater than your delai t*. Another interesting link is the F77 code Archi of C.A.H. Paul: http://www.ma.man.ac.uk/~chris/software.html Hope this helps. Didier -- _________________________________________________________________ Didier Pieroux Theoretical Nonlinear Optics, CP 231 Physics Department, Universite Libre de Bruxelles Bvd du Triomphe, B-1050 Brussels, Belgium Phone: ++ 32 2 650 5903, Fax: ++ 32 2 650 5824 http://www.ulb.ac.be/polytech/soa/IAP/iap.html _________________________________________________________________