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Re: Plot works in Mathematca 7 but not in Mathematica 8

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115855] Re: Plot works in Mathematca 7 but not in Mathematica 8
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Sun, 23 Jan 2011 05:34:16 -0500 (EST)

I also got an empty Plot in version 8, but I found two solutions.

First, the awkward one:

h = 1; a = 0.0001; kn = Pi/h; kr = 3.050;
ListPlot[pts =
   Table[{ki,
     Abs[((kn^2 - (kr + ki I)^2)*(4 h (Log[4 h/a] -
              NIntegrate[(1 - Exp[I (kr + ki I) y Cos[kn y]])/y, {y, 0,
                 2}]) +
           I/((kr + ki I) + kn) (Exp[I 2 ((kr + ki I) + kn) h] - 1) +
           I/((kr + ki I) - kn) (Exp[I 2 ((kr + ki I) - kn) h] -
              1)) - (kn^2 + (kr + ki I)^2)*
         NIntegrate[
          Exp[I (kr + ki I) y] Sin[kn y]/y, {y, 0,
           2}])]}, {ki, -0.23, -.10, .001}], Joined -> True]

Is that what the plot should look like?

If it is, you get a good approximation to the function with

f = Interpolation@pts;
Plot[f@ki, {ki, -.23, -.1}]

Finally, the simple solution:

h = 1; a = 0.0001 // Rationalize; kn = Pi/h; kr = 3.050 // Rationalize;
g[ki_?NumericQ] :=
  Abs[((kn^2 - (kr + ki I)^2)*(4 h (Log[4 h/a] -
           NIntegrate[(1 - Exp[I (kr + ki I) y Cos[kn y]])/y, {y, 0,
             2}]) + I/((kr + ki I) + kn) (Exp[
            I 2 ((kr + ki I) + kn) h] - 1) +
        I/((kr + ki I) - kn) (Exp[I 2 ((kr + ki I) - kn) h] -
           1)) - (kn^2 + (kr + ki I)^2)*
      NIntegrate[Exp[I (kr + ki I) y] Sin[kn y]/y, {y, 0, 2}])]
Plot[g@ki, {ki, -0.23, -.10}]

Bobby

On Sat, 22 Jan 2011 02:24:31 -0600, 1.156 <rob at piovere.com> wrote:

> I've found very little to complain about using Mathematica 8 but I just  
> ran into a
> Plot which only displays the two plot axes, no graph. Fortunately I
> still have Mathematica 7 installed and found that Mathematica 7 Plots  
> this same code nicely.
> Can anyone give me clues on what may make this work correctly in  
> Mathematica 8?
> Code below, thanks.
>
> ***************
> h = 1; a = 0.0001; kn = Pi/h; kr = 3.050;
> Plot[Abs[((kn^2 - (kr + ki I)^2)*
>       (4 h (Log[4 h/a] -
>       NIntegrate[(1 - Exp[I (kr + ki I) y Cos[kn y]])/y, {y, 0, 2}]) +
>         I/((kr + ki I) + kn) (Exp[I 2 ((kr + ki I) + kn) h] - 1) +
>         I/((kr + ki I) - kn) (Exp[I 2 ((kr + ki I) - kn) h] - 1) ) -
>      (kn^2 + (kr + ki I)^2)*
>       NIntegrate[
>        Exp[I (kr + ki I) y] Sin[kn y]/y, {y, 0, 2}])], {ki, -0.23, -.10}]


-- 
DrMajorBob at yahoo.com


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