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MathGroup Archive 2007

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Re: Paul Abbott Chebyshev Article

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79761] Re: Paul Abbott Chebyshev Article
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 3 Aug 2007 06:37:32 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <f8s2kq$161$1@smc.vnet.net>

Angela Kou wrote:
> Hi:
> 
> I'm trying to test Paul Abbott's code in his article on integral 
> equation solving using Chebyshev polynomials (Mathematica Journal 8(4)) 
> but Mathematica keeps giving me an error when I get to NIntegrate.  This 
> is the code:
> n=4; xs = N[Cos[Range[0, 2 n] Pi/(2 n)], 20];
> cs = Thread[Subscript[c, Range[0, n]]];
> lhs = cs.Table[Subscript[T, 2 i] (xs), {i, 0, n}];
> rhs = 1 + 1/Pi cs.Table[NIntegrate[Evaluate[Subscript[T, 2 i] (t)/((xs - 
> t)^2 + 1)], {t, -1, 1}, WorkingPrecision ->20], {i, 0, n}];
> 
> the last line of code keeps giving me the error that "NIntegrate::inumr: 
> The integrand (t Subscript[T,0])/(1+(1.0000000000000000000-t)^2) has 
> evaluated to non-numerical values for all sampling points in the region 
> with boundaries {{-1,0}}. >>
> 
> I'm not quite sure why this is the case?
> 
> Thanks,
> Angela Kou
> 

Every parameter, variable, symbol must have some explicit numerical 
values when you evaluate *NIntegrate*. In the code you provided, none of 
the T_i (i = 0, 1, ..., 4) have numerical values (they are not defined 
at all, indeed).

Compare the results returned by the following expressions:

With[{i = 0},
  NIntegrate[
   Evaluate[Subscript[T, 2 i] (t)/((xs - t)^2 + 1)], {t, -1, 1},
   WorkingPrecision -> 20]
  ]

versus

With[{i = 0},
  NIntegrate[
   Evaluate[Subscript[T, 2 i] (t)/((xs - t)^2 + 1)] /.
    Subscript[T, 0] -> 1, {t, -1, 1}, WorkingPrecision -> 20]
  ]

Regards,
Jean-Marc


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