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MathGroup Archive 2004

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Re: StruveH runtime error

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45680] Re: StruveH runtime error
  • From: vb at cybertester.com (Vladimir Bondarenko)
  • Date: Mon, 19 Jan 2004 05:15:23 -0500 (EST)
  • References: <buap11$mim$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Toshiyuki \(Toshi\) Meshii" <meshii at mech.fukui-u.ac.jp> wrote in message news:<buap11$mim$1 at smc.vnet.net>...

TM> StruveH[1,10^5]

TM> Microsoft Visual C++ Runtime Library Runtime Error!
TM> Program......\Mathkernel.exe
TM> abnormal program termination.
 
TM> Can someone help me on calculating StruveH functions 
TM> for large values by Mathematica?


I confirm that you re-discovered a bug in Mathematica 5 I
reported to Stephen Wolfram on 1 Sep 2001 22:26:38 in the
CHAPTER 1: Integration: Simplest Elementary Functions of
my memoir OPPORTUNITIES TO IMPROVE THE MATHKERNEL under
# 385 and # 467. For example, the entry # 467 refers to

   NProduct[StruveH[0, n], {n, 1, Infinity}]

In Mathematica 5.0, this expression invokes

   Runtime Error: Microsoft Visual C++ Runtime Library

I have already sent you report to support at wolfram.com .


The solution to your problem is to use asymptotic expansions:

StruveH[1,z] -> (2-Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi + O(1/z^(3/2))


In[1] := $Version

Out[1] = 5.0 for Microsoft Windows (June 11, 2003)


In[2] := (2 - Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi/.z -> 10^4//N//Timing

Out[2] = {0. Second, 0.643716}


In[3]:= (2-Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi/.z->10^5//N//Timing

Out[3]= {0. Second, 0.638339}


In[4]:= (2-Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi /.z ->10^1000000//N//Timing

Out[4]= {0.831 Second, 0.63662}


By the way, StruveH[1,z] satisfies the following ODE

In[5]:= DSolve[{z^2y''[z] + z y'[z] + (z^2 - 1)y[z] == 2/P z^2,\
        y[0] == 0, y'[0] == 0}, y[z], z]

(* unfortunately, Mathematica 5 fails here *)

Out[5]= {}   (* expected:  StruveH[1, z] *)

which is yet another bug.


Best wishes,

Vladimir Bondarenko

GEMM architect
Co-founder, CEO, Mathematical Director
Cyber Tester, LLC

http://www.cybertester.com/
http://www.CAS-testing.org/

................................................................


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