## Numerical Integration; Tanh-Sinh Quadrature v. 4.42

Back to Newton and Excel.

The Tanh-Sinh quadrature workbook has been enhanced as follows:

1. The Tanh-Sinh integrator in the workbook may be the fastest finite-interval integrator on the planet!!
2. The speed of the DE programs has been doubled.
3. A fast finite interval program TINT has been added. It runs at over twice the speed of the Gauss-Kronrod program.
4. The speed of the Gauss-Kronrod program has been improved through modifications developed by Berntsen, Espelid and Sorevik.
5. The Romberg integrator, written by the author, may be the fastest and most accurate Romberg integrator on the planet!!
6. Now includes over 1200 test integrals with true results. This may be the largest set of diverse test integrals available at no cost. It includes several of the “standard” sets of test integrals in wide use.
7. The Plotter worksheet now shows two plots: the plot of the selected function over the finite interval (a,b), and the plot of the selected function after being transformed by the Tanh-Sinh function.
8. Minor change to allow compatibility with Excel 2007.
9. Minor correction.

Graeme Dennes

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### 10 Responses to Numerical Integration; Tanh-Sinh Quadrature v. 4.42

1. Dave McCutchan says:

As absolutely no one else has put an example of using this quadrature method in Excel on the web it I would help a lot of folks to see an example ( non-VBA for us dummies!)

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2. dougaj4 says:

You can find a list of posts related to this spreadsheet at:
and these give more background information.
But really the best bet is to download the latest version and look at the many examples in there. Note that you don’t need any VBA to use the spreadsheet, you just enter the function in the same way as a built in Excel function, but if you are interested in the coding it is all open source, and very well documented by the author (Graeme Dennes).

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3. Dave McCutchan says:

I am writing a book on Excel Math use, hopefully to provide students of color or disadvantaged to see how it could stimulate their discovery in science, make better decisions and maybe get a fun rewarding job, as I had as an engineer . So I need to show how to execute a problem.

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• dougaj4 says:

I am not sure what you are looking for exactly, some practical examples, or working through the maths on the spreadsheet?

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4. Dave says:

I need practical examples executed on spreadsheet without VBA to show how the method works.

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• dougaj4 says:

Dave – I’m having a look at this, and making some progress, although I’m not sure how useful it will be for a student text as the procedure is fairly complex compared with the more widely known numerical integration methods, and I’m struggling to understand how it all works myself.
Could you send your email contact details to dougaj4 at the gmail address, and I’ll send a spreadsheet to have a look at when I have tidied things up.

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• Dave says:

That would be wonderful! Lots of talk, much of it confusing, on the web. I set up a spreadsheet with all the abscissas and weights, but still get the wrong answer, A lot of people could benefit if you posted that sheet

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