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MathGroup Archive 1996

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Re: NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2987] Re: NIntegrate
  • From: moore.550 at postbox.acs.ohio-state.edu (Todd Moore)
  • Date: Fri, 19 Jan 1996 02:26:09 -0500
  • Organization: The Ohio State University

In article <4dkst6$gr0 at dragonfly.wri.com> Drib <Ian.Barringer at brunel.ac.uk> writes:
>Path:
>magnus.acs.ohio-state.edu!math.ohio-state.edu!uwm.edu!chi-news.cic.net!dragonfly
>.wri.com!usenet
>From: Drib <Ian.Barringer at brunel.ac.uk>
To: mathgroup at smc.vnet.net
>Newsgroups: comp.soft-sys.math.mathematica
>Subject: NIntegrate
>Date: 18 Jan 1996 07:29:42 GMT
>Organization: Steven M. Christensen and Associates, Inc. and MathSolutions, Inc.
>Lines: 23
>Approved: Steven M. Christensen <steve at smc.vnet.net>, Moderator
>Message-ID: <4dkst6$gr0 at dragonfly.wri.com>
>NNTP-Posting-Host: smc.vnet.net


>Hi,
>        Could someone offer an indepth explaination about how
>NIntegrate achieves its results. I am currently using it to obtain
>some numerics for a comparison with results I have obtained analytically
>in my research. I feel I should know how they are obtained before
>relying on them.

>All donations gratefully received
>                        Ian.

> 
>--------------------------
>Ian.Barringer at Brunel.ac.uk

 as I recall, NIntegrate approximates an integral in exactly the same way that 
a person would, through trapezoidal approximation.

 so for the function f[x] it selects  points on f[x] and finds the area of all 
the trapizoids formed by connecting these points to eachother and the x axis 
over the specified range of x {x,a,b}.

Mathmatica continues to refine these trapezoids by making them thinner, and 
there by getting a more accurate approximation. It continues to refine the 
approximations untill it reaches the prescribed accuracy.

Hope this helps,
Todd Moore



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