Error function

[Timusop]

I understand the basis of the math behind the error function (

http://mathworld.wolfram.com/Erf.html)

however...

Can anyone please explain in "engineering terms" what the error function is and how can I use it? I have found the erf(h/sqrt(2*s)) in the derivation of formula which involves gaussian distribution.

Thanks

 

[IRstuff]

I use it for just that purpose.

TTFN

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[Timusop]

I am not sure what "t" is in the error function?

http://en.wikipedia.org/wiki/Error_function

Any suggestions, thanks.

 

[Wrenchbender]

The only application i've ever seen for the Error Function is in heat conduction (or in atomic diffusion, mathematically similar phenomena). Its used to describe the transcient temperature (or concentration) gradient as a function of distance beneath the surface, x, and time, t, for a semi-infinite solid. The free surface of this solid is exposed to a different temperature (or atomic concentration) than the bulk. In the analysis the surface (where x = 0) temperature never changes. Over time (t increasing) the temperature curve inside the sold flatens out and approaches the surface. The shape of this curve is some whacked out integral that they named erf.

 

[Timusop]

Thanks Wrenchbender, the application I am looking at is a is based on a rather messy equation of asperity contact pressures. I has nothing to do with 'time', the term in the equation is:

1-erf(h/sqrt(2*s))

I want to evaluate this equation numerically, how could I do that? Thanks, I am getting somewhere with this I think.

 

[Occupant]

As you can see , the "t" means nothing, it is just a place holder. You can solve either the integral, where your formula is the "t" as in erf(formula), use the "erf" function directly as you have written it or find a series expansion some where.

 

[Occupant]

I didn't say that right. "x" is obviously the formula and not the "t" in the integral.

 

[zekeman]

"1-erf(h/sqrt(2*s))"

Only you can tell what h and s are. The function is a solution to

d^2z/dh^2=2*dz/ds

which is a partial differential equation where I use the symbol "d" for the partial and d^2 the second partial.

Your link defines erf and from that and the parameters it should be easy to calculate or use tables for evaluation.

 

[IRstuff]

t is the variable of integration

erf([σ]/sqrt(2)) = 95.45%, which is the same as ±2[σ], so the form of the erf is identical to the integral from -2 to +[σ] of a gaussian distribution.



TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[Timusop]

I understand that the error function is encountered when integrating the normal distribtution, but still not fully convinced of how it applies to engineering. Thanks for all you help everyone.

P.S. Occupant, what software did you use to do the err evaluation? Is it MathCAD? I am currently using SMath Studio.

 

[IRstuff]

Ditto, Mathcad.

SMath's GUI is more complicated than Mathcad's.

I guess I don't understand your comment here. Since you know what the error function does related to normal distributions, your specific question has been answered. The fact that you might not have a need to use it in your engineering doesn't mean that others also don't.

As I indicated above, I routinely use ERF in calculating probable distributions in my engineering area. A specific example is how large a physical area a munition might hit, given its dispersion, which is a measure of its statistical spread. There are, of course, other functions within Mathcad that do similar things, but ERF has the form that I prefer for that particular analysis.

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize