Update 27 Nov 2018: Version 4.41 now available from the link below, with minor modifications for compatibility with Excel 2007.

I recently received a new version (4.4) of the numerical integration spreadsheet by Graeme Dennes which is now available for download from:

Tanh_Sinh Quadrature.

The new spreadsheet includes significant improvements in the performance of several functions, as well as new functions:

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

(1) A faster Tanh-Sinh program has been implemented, increasing the speed by around 50 percent, and the speed of the DE programs has been doubled.

(2) A fast finite interval program TINT has been added. It runs at over twice the speed of the Gauss-Kronrod program.

(3) The speed of the Gauss-Kronrod program has been improved through modifications developed by Berntsen, Espelid and Sorevik.

(4) The Plotter worksheet now shows two plots: the plot of the selected function over the finite interval (a,b), and the plot of the function after being transformed by the Tanh-Sinh function.

(5) Now includes over 1200 test integrals with results correct to 15 significant digits. This may be the largest set of diverse test integrals and results available at no cost. It includes several of the “standard” sets of test integrals in wide use.

(6) The Romberg integrator, written by the author, may be the fastest and most accurate Romberg integrator available. Advice to the contrary would be most welcome.

(7) Minor change to allow compatibility with Excel 2007.

Graeme Dennes