Re: NDSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg65687] Re: NDSolve
- From: bghiggins at ucdavis.edu
- Date: Sun, 16 Apr 2006 01:44:44 -0400 (EDT)
- References: <e1nnch$lnr$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
You can evaluate the derivate from the solution in several ways. The
first way (not the most convenient) is
sol1 = NDSolve[{y''[x] == Cos[y[x]], y[0] == 1, y'[0] == 0}, y[x], {x,
1, 10}]
{{y[x] -> InterpolatingFunction[{{1., 10.}}, <>][x]}}
Then to determine the derivative at a point
D[y[x]/.sol1,x]/.x->2.
{0.519544}
If you are interested in the value of the derivative and plotting the
derivative (i.e a phase plot), then it is more convienet to get the
rule for the solution in the form y->InterpolationFunction rather than
y[x]->InterpolationFunction as follows:
sol2 = NDSolve[{y''[x] == Cos[y[x]], y[0] == 1, y'[0] == 0}, y, {x, 1,
10}]
{{y -> InterpolatingFunction[{{1., 10.}}, <>]}}
Then to find the derivative we simply evaluate
y'[2.]/.sol2
{0.519544}
Hope this helps,
Cheers,
Brian