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Re: How to get data from solvin' numerically differential

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104175] Re: [mg104129] How to get data from solvin' numerically differential
  • From: ÐÐÑÐÐÐ ÐÐÐÐÐÐÐÐÐ <shalm89 at gmail.com>
  • Date: Thu, 22 Oct 2009 02:17:14 -0400 (EDT)
  • References: <520d9b5f0910200910x2d7ac379i9b03eeec3cc5dd30@mail.gmail.com>

Thank you, Bob.

2009/10/21 Bob Hanlon <hanlonr at cox.net>

>
> s = y /. NDSolve[
>     {y'[x] == y[x] Cos[x + y[x]], y[0] == 1},
>     y, {x, 0, 30}][[1]];
>
> The integral of the interpolation function is
>
> int[x_?NumericQ /; 0 <= x <= 30] :=
>  Integrate[s[t], {t, 0, x}]
>
> Plotting the function and its integral
>
> Show[{p1 = Plot[s[x], {x, 0, 30},
>    PlotRange -> All],
>  p2 = Plot[int[x], {x, 0, 30}]},
>  Frame -> True, Axes -> False]
>
> The plots were done separately to facilitate extraction of the points.
> Extracting the points from the plots
>
> pts1 = Cases[p1, {_?NumericQ, _?NumericQ}, {6}];
>
> pts2 = Cases[p2, {_?NumericQ, _?NumericQ}, {6}];
>
> If you want to see the points displayed, remove the semi-colons that are
> suppressing their display. However, there are lots of points:
>
> Length /@ {pts1, pts2}
>
> {1281,634}
>
> Showing that the points represent the original curves
>
> ListLinePlot[{pts1, pts2}, PlotRange -> All, Frame -> True, Axes -> False=
]
>
>
> Bob Hanlon
>
> ---- "=D0=9C=D0=B8=D1=85=D0=B0=D0=B8=D0=BB =D0=A8=D0=B0=D0=BB=D0=B0=D0=B3=
=D0=B8=D0=BD=D0=BE=D0=B2" <shalm89 at gmail.com> wrote:
>
> =============
> Bob, thank you for your answer.
> Should all the values(points of numerical solution of differential
> equation)
> appear after the command ListLinePlot?
> I can't see values of this points.
> Do you know, how can I integrate this interpolated function?
> Thank you again.
> Best regards,  Mikhail Shalaginov
>
>
> 2009/10/20 Bob Hanlon <hanlonr at cox.net>
>
> >
> > s = y /. NDSolve[
> >     {y'[x] == y[x] Cos[x + y[x]], y[0] == 1},
> >     y, {x, 0, 30}][[1]];
> >
> > p = Plot[s[x], {x, 0, 30}, PlotRange -> All,
> >  Frame -> True, Axes -> False]
> >
> > Extracting the points from the plot
> >
> > pts = Cases[p, {_?NumericQ, _?NumericQ}, {6}];
> >
> > Length[pts]
> >
> > 1281
> >
> > ListLinePlot[pts, PlotRange -> All,
> >  Frame -> True, Axes -> False]
> >
> >
> > Bob Hanlon
> >
> > ---- "=D0=9C=D0=B8=D1=85=D0=B0=D0=B8=D0=BB =D0=A8=D0=B0=D0=BB=D0=B0=D0=
=B3=D0=B8=D0=BD=D0=BE=D0=B2" <shalm89 at gmail.com> wrote:
> >
> > =============
> > Hi,
> > Mathematica solves numerically differential equation and makes
> > interpolation. I can plot this interpolating function. Can I save all
> > the points in a file or somehow get this data?
> > Best regards, Mikhail Shalaginov.
> >
> >
>
> --
>
> Bob Hanlon
>
>


--
Best regards, Mikhail Shalaginov.



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