From: Didier Pieroux <dpieroux@ulb.ac.be>
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
-- 
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     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 
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