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$gr0 at dragonfly.wri.com> Drib <Ian.Barringer at brunel.ac.uk> writes:
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>From: Drib <Ian.Barringer at brunel.ac.uk>
To: mathgroup at smc.vnet.net
>Newsgroups: comp.soft-sys.math.mathematica
>Subject: NIntegrate
>Date: 18 Jan 1996 07:29:42 GMT
>Organization: Steven M. Christensen and Associates, Inc. and MathSolutions, Inc.
>Lines: 23
>Approved: Steven M. Christensen <steve at smc.vnet.net>, Moderator
>Message-ID: <4dkst6$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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