Re: Delay Differential Equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg8815] Re: [mg8798] Delay Differential Equations*From*: David Withoff <withoff>*Date*: Fri, 26 Sep 1997 00:33:39 -0400*Sender*: owner-wri-mathgroup at wolfram.com

> Can I solve DDE of the form > > x'(t) = F(t, x(t), x(t-a)) > > with NDSolve? It appears it is not able to refer back to its own > solution while it is still in progress. > > Matthias Weiss > mweiss at math.niu.edu There are two methods that I have used for delay differential equations: 1) Solve the equation in steps, using some initial condition in the first step, then using the solution from that first step in the next step, and so forth. A program to do this is usually only a few lines long. 2) Solve the system self-consistently. Guess a solution, use that solution in place of x(t-a) to get a new solution, use the new solution in place of x(t-a) to get a newer solution, and so forth. A program to do this is usually only a few lines long too. There is no guarantee that this method will converge, or that it will converge very fast, but this method has worked very well in the examples that I've tried. It is likely that a delay differential equation solver will be added for some future version of Mathematica, but in the meantime I've found the methods above to be fairly straightfoward. Dave Withoff Wolfram Research