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PhilipOakley1-Visitor
1-Visitor
July 17, 2014
Question

Is Mathcad considering newer advanced integration techniques?

  • July 17, 2014
  • 1 reply
  • 1536 views

Hi,

I've just seen an article on a high accuracy numerical integration method that I hadn't heard of in http://www.codeproject.com/Articles/31550/Fast-Numerical-Integration (links to [3])

This is the techniques of "The double-exponential transformation in numerical analysis" by Masatake Mori and Masaaki Sugihara in the Journal of Computational and Applied Mathematics, volume 127 (2001), pages 287-296 [1]. Its discovery is in [2].

I've often seen mathcad integrals "fail" when folk forget that they have plotted some log-log function that ends up as a spike on a lin-lin plot. I'm not yet sure how well this technique would work within mathcad, but I thought it worth sharing.

Has anyone else used or studied this method? If it overcomes the lo-log problem it would be great.

Philip.

refs:

[1] http://www.sciencedirect.com/science/article/pii/S037704270000501X (I was able to download it)

[2] http://www.kurims.kyoto-u.ac.jp/~okamoto/paper/Publ_RIMS_DE/41-4-38.pdf Discovery of the Double Exponential Transformation and Its Developments.

[3] http://www.johndcook.com/double_exponential_integration.html

1 reply

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RichardJ19-Tanzanite
19-Tanzanite
July 17, 2014

How about we just get what we have in MC15 into Prime. Including the ability to choose the integration method. Then let's worry about the stuff we've all been asking for for a decade and still don't have. Then we can get to new stuff. At the current rate of progess we can revisit this topic in about 30 years.

P
PhilipOakley1-VisitorAuthor
1-Visitor
July 18, 2014

Actually, I was more using the post as a marker so that it's still on the to-do list in 20 years (theres still stuff on my list from 15 years ago ;-).

Plus bring the method to the attention of others, some of whom may want to create an EFI for V15 so we can try it in situ. (I would but it would only be added to the back log of home jobs I keep promising to do !)

Either way, the technique looked interesting.

Philip

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