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*From*: Joel Rauber <Joel_Rauber@SDSTATE.EDU>*Date*: Fri, 9 Feb 2001 09:39:38 -0600

A partial answer to this question is that one must develope a finite

difference scheme to approximate the laplacian in these coordinates. Some

references that are readily available and may be of partial help.

Abromowitz & Stegun: section 25 around page 877

This is a Dover publication titles "Handbook of Mathematical Functions"

CRC 30th ed. math tables around page 705-715, the section on numerical

differentiation.

Hope this may be of some help.

Joel Rauber

-----Original Message-----

From: phys-l@lists.nau.edu: Forum for Physics Educators

[mailto:PHYS-L@lists.nau.edu]On Behalf Of Ludwik Kowalski

Sent: Friday, February 09, 2001 8:28 AM

To: PHYS-L@lists.nau.edu

Subject: Re: visualizing fields near charged objects

And what is the corresponding formula for "a" when it has

six neighbors (3-dim)? Suppose f and g are added in the phi

direction. I do not trust myself in trying to answer this

question on the basis of the general theoretical formula.

Ludwik Kowalski

John Mallinckrodt wrote:

On Fri, 9 Feb 2001, John Mallinckrodt wrote:

where r_a is the radial index for cell a. Setting the Laplacian =

0 and solving for a we get

a = (b+c+d+e)/4 + (c-e)/(2*r_a)

Oops! I should have said:

a = [ (b+c+d+e) + (c-e)/(2*r_a) ]/4

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