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!
>
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...
>
>
> 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

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