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MathGroup Archive 2002

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Re: numerical compuation of integral with unbounded limits

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33817] Re: numerical compuation of integral with unbounded limits
  • From: "Dugmore Biyana" <DBiyana at btech.tktech.ac.za>
  • Date: Fri, 19 Apr 2002 02:27:34 -0400 (EDT)
  • Organization: Eastern Cape Technikon
  • Sender: owner-wri-mathgroup at wolfram.com

Attached is the outline of the specific problem that I have
DM Biyana
dbiyana at btech.tktech.ac.za


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Notebook[{
Cell[BoxData[
    \(TraditionalForm\`Need\ to\ find\ \ numerical\ \ \ integration\ or\ \
approximation\ of\ the\ following\)], "Input"],

Cell[BoxData[
    \(\(1\/\(2  \[Pi]\)\) \(\[Integral]\_\(P = \ K\)\%\[Infinity]\(\((P - 
                  K)\)\/P\^\(-1.5\)\) \(\[Integral]\_\(-\[Infinity]\)\%\
\[Infinity] I \((\((\[Eta]\^2 + 1\/4)\) T/2)\)*
              Cos[Log[P]*\[Eta]] \[DifferentialD]\[Eta] \[DifferentialD]P\)\)\
\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`where\)], "Input"],

Cell[BoxData[
    \(I \((\[Lambda])\) = Exp[N + M*\[Nu]*\((\[Lambda]/T)\)]\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`with\)], "Input"],

Cell[BoxData[
    \(N = \((2*\[Alpha]*m)\)*
        Log[\(2*\[Gamma]*Exp[\((\[Alpha] - \[Gamma])\)*\((T/2)\)]\)\/g]/\
\[Zeta]\^2\)], "Input"],

Cell[BoxData[
    \(M = \(\(-2\)*\((1 - Exp[\(-\[Gamma]\)*T])\)\)\/g\)], "Input"],

Cell[BoxData[
    \(g = 
      2*\[Gamma] + \((\[Alpha] - \[Gamma])\)*\((1 - 
              Exp[\(-\[Gamma]\)*T])\)\)], "Input"],

Cell[BoxData[
    \(\[Gamma] = 
      Sqrt[\((\[Alpha]^2)\) + 2*\((\[Lambda]/T)\)*\((\[Zeta]^2)\)]\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`The\ following\ parameters\ can\ be\ used\)], "Input"],

Cell[BoxData[
    \(\[Alpha] = 4, T = 0.5, \[Zeta] = 0.4, m = \(\[Nu] = 0.09\), 
    K = 100\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`My\ problem\ in\ using\ \ a\ \ numerical\ quadrature\ \
is\ with\ the\ limits, \ 
    the\ answers\ I\ \ get\ \ are\ very\ sensitive\ to\ \ the\ finite\ limits\
\ I\ \(\(try\)\(.\)\)\)], "Input"]
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(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)




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