Numerical Integration; Tanh-Sinh Quadrature v. 4.2

The latest version (4.2) of the numerical integration spreadsheet by Graeme Dennes is now available for download from Tanh_Sinh Quadrature.

For more details of the background see: Faster Integration with the Tanh-Sinh Method and subsequent posts on this subject.

In addition to the code and examples on the use of Tanh-Sinh quadrature and a number of other techniques, the download file contains examples and thoroughly documented code for a range of other spreadsheet and VBA functions, including:

  • Dynamic linking of graphs to function results, without writing the results to the spreadsheet
  • Evaluating functions entered as text on the spreadsheet
  • Timing of function execution time with a high precision timer
  • Accurate determination of processor constants, such as maximum an minimum floating point values.
  • VBA code for the complete range of standard trigonometry functions
  • Examples of incorporating the quadrature functions in other routines.

The revisions included in Ver. 4.2 are listed below.  In the next post in this series I will look in more detail at how these functions can be incorporated in other spreadsheets.

Version 4.2 Release Notes

  1. Following a private suggestion, all quadrature programs now provide the number of function evaluations as a more useful performance metric.
  2. The Romberg program runs in 30 percent of the time taken by the previous (V4.1) release, and accuracy averages only one digit less than Tanh-Sinh. The Romberg algorithm implemented herein by the author may be the fastest and most accurate to date.
  3. The function plotter is located on a separate worksheet for convenience.
  4. Finite interval test functions total 400, which may be the largest set of diverse test integrals available (with answers) at no cost.

Graeme Dennes


This entry was posted in Excel, Maths, Newton, Numerical integration, UDFs, VBA and tagged , , , , , , , , . Bookmark the permalink.

2 Responses to Numerical Integration; Tanh-Sinh Quadrature v. 4.2

  1. Dann Corbit says:

    What a marvelous work this is. I am surprised at how comprehensive the review is. Thank you for your efforts.


  2. Graeme Dennes says:

    Hello Dann – thank you for your positive feedback. I’m pleased you’ve found the workbook to be of interest, and hopefully it proves to be of value to you.
    For information, a new release of the workbook should appear over the next few days.
    Thanks Dann.


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