Re: Integrating Differential Equations with Time Delay

*To*: mathgroup at smc.vnet.net*Subject*: [mg75642] Re: Integrating Differential Equations with Time Delay*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Mon, 7 May 2007 05:38:29 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <f1eqpt$59j$1@smc.vnet.net> <f1hmhp$pij$1@smc.vnet.net> <f1jq67$3jt$1@smc.vnet.net>

rob wrote: > Jean-Marc Gulliet wrote: > >> Haider Arafat wrote: >> >>> I am not able to use NDSolve to integrate a differential equation of the >>> form >>> >>> u''(t) + a u(t) == b u(t-tau); >>> u(0) == u0; >>> u'(0)==udot0; >>> >>> where tau, a, and b are all constants. Is there any way to numerically >>> integrate this type of equations >>> in Mathematica. >>> >>> Any help is appreciated, >>> >>> Haider Arafat >> >> Allan Hayes's package NDelayDSolve should be of interest: "The package >> extends the built-in function NDSolve to deal with delay differential >> equations." See "Delay-Differential Equations" at >> http://library.wolfram.com/infocenter/MathSource/725/ >> >> Regards, >> Jean-Marc >> > > Hi, I got this package and I believe it loads ok. But I > can't seem to get it to work. I read the text in the top of > the NDelayDSolve.m file (I found no other sources of > documentation for it) and I've tried many ways to get it to > work. Here's what I did: > > a=1; b=1; tau=6; u0=0; udot0=0; > > <<"NDelayDSolve`" > > eqns={u''[t] + a u[t] == b u[t - tau], u[0] == u0, u'[0] == > udot0} > > sol = NDelayDSolve[eqns, {u -> (#1 &)}, {t, 0, 5}] > > But I get the following err. message (snipped) > > NDSolve::"ndnco" : "The number of constraints (4) (initial > conditions) \is not equal to the total differential order of > the system (2)..... > > I tried all sorts of groupings of the DE and the two > constraints and with most other attempts the error message > goes away but the sol= statement is just repeated and not > evaluated. In short it thinks my 2 constraints are 4 or it > doesn't do anything at all. Could you perhaps suggest > something that would make this system work? Thank you. > I am not really familiar with the package, but the following expression might return the solution you are looking for. sol = NDelayDSolve[{Derivative[2][u][t] + a*u[t] == b*u[t - tau]}, {u -> (#1 & ), Derivative[1][u] -> (0 & )}, {t, 0, 5}] Plot[{u[t] /. sol[[1]], Derivative[1][u][t] /. sol[[1]]}, {t, 0, 5}] Regards, Jean-Marc