Re: Evaluation of AiryAi on the complex plane
- To: mathgroup at smc.vnet.net
- Subject: [mg44955] Re: Evaluation of AiryAi on the complex plane
- From: "Kevin J. McCann" <kjm at KevinMcCann.com>
- Date: Thu, 11 Dec 2003 05:28:01 -0500 (EST)
- References: <br6oss$2lg$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I think this is a problem of numerics. I tried the following
Plot[Abs[AiryAi[x+0.01I],{x,10,12}];
The result shows an exponentially dropping value up to about 10.8 at which
point it abruptly drops to zero. I suspect that this is a boundary for the
computational method used. The values are ~10^-11; so for many this is a
good approximation to zero, but obviously not for everyone.
Kevin
"Mauricio Bedoya" <mbedoya at tutopia.com> wrote in message
news:br6oss$2lg$1 at smc.vnet.net...
> Hello:
>
> I'm in trouble evaluating the AiryAi function. I need to evaluate it
> around the point (11.18,0) or (11.18 + I 0.0). When I sweep the real
> axis there is no problem [1], it has a value of 2 10^-12 on all the
> range.
>
> But when I choose a range on a complex line [2], the function throws a
> 0 value on all the range.
>
> when I evaluate the function [3] I obtain 0 in the complex plane
> around 11.18 and 2.31151*10^-12 in 11.18, no matter how close I am
> from 11.18 + 0.0 I.
>
> This doesn't happen around the points 10.03 + 0.0 I and 23.52 + 0.0 I.
>
> I work in mathemathica 4.1.2.0.
>
> I have tried to evaluate the Ai function in the version 3 and the
> result is 0 in the complex plane, but when I plot the function with
> complex values I obtain values different from 0 and also the absolute
> value of the function is continuous. I think that there is a problem
> with the evaluation of the function around 11.18 because I plotted the
> function in mathematica 3 with no problems but I couldn't evaluate it.
> In the version 4 I couldn't plot or evaluate it.
>
> I would be grateful if someone could help me with this problem.
>
>
> Mauricio Bedoya
>
> List of commands
> [1] Plot[{AiryAi[11.18 + x]}, {x, 0, 10^-100}, PlotRange -> {All, {0,
> 10^-11}}]
> [2] Plot[{AiryAi[11.18 + x I]}, {x, 0, 10^-100}, PlotRange -> {All,
> {0, 10^-11}}]
> [3] Abs[ai[11.18]]
> Abs[ai[11.18 + 0 10^-11 I]]
>