Re: NDSolve solutions

*To*: mathgroup at smc.vnet.net*Subject*: [mg125087] Re: NDSolve solutions*From*: Niles <niels.martinsen at gmail.com>*Date*: Tue, 21 Feb 2012 06:10:57 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jhsto5$nht$1@smc.vnet.net>

On Feb 20, 8:46 am, Niles <niels.martin... at gmail.com> wrote: > Hi > > I have solved an ODE using NDSolve, and I plot the solution like this: > > ParametricPlot[{z[t], z'[t]} /. solution, {t, 0, 2 maxTime}, PlotRange > -> {{0, 0.2}, {0, 450}}, AspectRatio -> 0.75] > > The curve shown (the velocity as a function of position) I want to use > in a new mathematical expression. How can I do that? If I use z'[t], > then it is as a function of time, which is no good to me. > > I appreciate your help. > > Best regards, > Niles. To clarify, what I have is a system of ODEs of the form dx/dt = v dv/dt = a = C*f(x), where C denotes a constant and f(x) is some function of x. This system is easy to solve using e.g. NDSolve[x''[t] == -C*f(x), x[0] == 0, x'[0] == 0}, x, {t, 0, tMax}]; The solution x[t] (or rather, its derivative x'[t]) I need to use in the following expression: B(x) = A + v(x) where A denotes a constant and v(x) is the velocity as a function of position x. But please note that v is as a function of x, not t. What should I do to achieve this? Best regards, Niles.