Re: Help required on differential equation

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1918] Re: Help required on differential equation*From*: Christian.Jost at epc.u-psud.fr (Christian Jost)*Date*: Fri, 18 Aug 1995 02:14:36 -0400*Organization*: Universite Paris-Sud XI

I tried to send this directly, but it was returned (user unknown). In article <DDDr09.AzA at wri.com>, Dr Brian Hunton tel 270502 <hunton at news.ox.ac.uk> wrote: > Hello all! > > Please help! I have a differential equation that I solve numerically wi= th > Mathematica. This gives me my interpolating function f[x] which I can h= appily > plot. Now I want to plot f''[x] over the same range, but I'm having all= sorts > of bother. Can anyone help? I'd be very grateful... > > Thanks in advance, > > Brian Hunton. I am just thinking aloud, but maybe that helps. You have an ordinary differential equation dx/dt =3D f(x(t)) (lets assume the autonomous case) and you want to plot d2x/d2t, right? The function x you got via numerical solution, and df(x)/dx should also b= e no problem. Then applying the chain rule you would get d2x/d2t =3D d/dt dx/dt =3D d/dt f(x(t)) =3D df(x)/dx dx/dt =3D df(x)/d= x f(x) and knowing x you can plot this function. Example: dx/dt =3D r(1-x/K)x (the logistic growth function) d2x(t)/d2t =3D d/dx (r(1-x/K)x) dx(t)/dt =3D (r - 2 r x(t)/K) r (1-x(t)/K) x(t) which is a function of x(t) which you got by numerical solution. Hope that helps, Christian. --=20 Christian Jost, Universit=E9 Paris-Sud XI, Orsay, France jost at psisun.u-psud.fr