Re: needed.

• To: mathgroup at smc.vnet.net
• Subject: [mg127058] Re: needed.
• From: "djmpark" <djmpark at comcast.net>
• Date: Wed, 27 Jun 2012 04:11:10 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <23314523.14289.1340701923445.JavaMail.root@m06>

```You could try this:

Plot[Exp[8*(10 - Abs[10 - 20000*x])]*(1 -
Erf[(8*(10 - Abs[10 - 20000*x]))^(1/2)]), {x, 0, 1*10^(-3)},
PlotRange -> Full,
WorkingPrecision -> 6]

And then maybe someone can explain why MachinePrecision fails but a
WorkingPrecision as low as 6 works.

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/index.html

From: Cyril [mailto:cyril.stephanos at gmail.com]

Hi everyone

I am using the error function as part of differential equations I am solving
with NDSolve.
Unfortunately, for certain parameters, the error function Erf[] starts
oscillating and yielding wrong values.

The oscillation does not show when I plot the error function itself, but
when I plot this expression

Plot[Exp[8*(10 - Abs[10 - 20000*x])]*(1 - Erf[(8*(10 - Abs[10 -
20000*x]))^(1/2)]), {x, 0, 1*10^(-3)}, PlotRange -> Full]

it becomes visible.

When I do the integration for error function with NDSolve manually and plot
the expression, the oscillation vanishes for high values of PrecisionGoal
and WorkingPrecision, e.g.

Plot[ Exp[8*(10 - Abs[10 - 20000*x])]*(1 - NIntegrate[ 2/Sqrt[Pi] Exp[-t^2],
{t, 0, (8*(10 - Abs[10 - 20000*x]))^(1/2)}, PrecisionGoal -> 40,
WorkingPrecision -> 40]), {x, 0, 1*10^(-3)}, PlotRange -> Full]

The oscillation of Erf[] is not only visible in the plot, it also leads to
wrong results in my calculations.

I tried to increase the precision of Erf[] by using N[Erf[],n] with very
high values for n - as described in the Mathematica help - but it does not
change anything.

Solving the Integral for the error function manually with NDSolve yields two
problems. It is very slow - it takes about three minutes on my computer (I
have to solve many equations) - whereas Erf[] is much faster. And it seems
that I cannot use NDSolve as part of an equation I want to solve with
NDSolve itself.

Is there a possibility to increase the precision of Erf[] and obtain more
accurate results?

Thank you in advance for your help.

Best regards
Cyril

```

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