Mathematica - Singularity handling in NIntegrate

Author

Singularity handling in NIntegrate

Andrew Moylan

2006-10-30, 7:43 pm

Hi all,

I've been searching around for information about the particular
method(s) that NIntegrate uses to handle singularities at the endpoints
of a numerical integration. In particular,

1. How is the SingularityDepth option used? Is it just the number of
recursive bisections of the first/last subinterval of integration
before a singularity is assumed?

2. What is/are the coordinate transformation(s) used when a singularity
is detected?

Thanks for any help you can give me with these questions.

Cheers,

Andrew

dimitris

2006-10-30, 7:43 pm

Information[SingularityDepth]
"SingularityDepth is an option for NIntegrate. SingularityDepth -> n
specifies that n recursive subdivisions can be done before
a change of variable is used at the endpoints of the interval of
integration."
Attributes[SingularityDepth] = {Protected}

See

http://groups.google.com/group/comp...223cb3882539ac8

http://library.wolfram.com/infocenter/Conferences/5365/

Hope these helps.

Regards
Dimitris

Andrew Moylan wrote:
> Hi all,
>
> I've been searching around for information about the particular
> method(s) that NIntegrate uses to handle singularities at the endpoints
> of a numerical integration. In particular,
>
> 1. How is the SingularityDepth option used? Is it just the number of
> recursive bisections of the first/last subinterval of integration
> before a singularity is assumed?
>
> 2. What is/are the coordinate transformation(s) used when a singularity
> is detected?
>
> Thanks for any help you can give me with these questions.
>
> Cheers,
>
> Andrew

Andrew Moylan

2006-10-30, 7:43 pm

Thanks Dimitris,

I've had a look at those sources. Actually, that previous thread that
you linked to was also started by me ;-).

Anton's response does suggest that the answer to my first question is
just "yes". It's really the second question (what are the coordinate
transformations used when a singularity is detected?) that I'm most
interested in. (Anton's response describes the compactifying
transformation used for infinite regions of integration.)

Can anyone shed any light on this second question?

Andrew

dimitris wrote:[color=darkred]
> Information[SingularityDepth]
> "SingularityDepth is an option for NIntegrate. SingularityDepth -> n
> specifies that n recursive subdivisions can be done before
> a change of variable is used at the endpoints of the interval of
> integration."
> Attributes[SingularityDepth] = {Protected}
>
> See
>
> http://groups.google.com/group/comp...223cb3882539ac8
>
> http://library.wolfram.com/infocenter/Conferences/5365/
>
> Hope these helps.
>
> Regards
> Dimitris
>
>
>
> Andrew Moylan wrote:

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