"Both engineers and computational scientists alike will benefit greatly from having a standard test set for Initial Value Problems (IVPs) which includes documentation of the test problems, experimental results from a number of proven solvers, and Fortran subroutines providing a common interface to the defining problem functions. Engineers will be able to see at a glance which methods will be most effective for their class of problems. Researchers will be able to compare their new methods with the results of existing ones without incurring additional programming workload; they will have a reference with which their colleagues are familiar. This test set tries to fulfill these demands and tries to set a standard for IVP solver testing."
Found on John Butcher's page https://www.jcbutcher.com/rkclub

Mentioned on the MoHP forum https://www.hpmuseum.org/forum/thread-16122-post-154062.html#pid154062

The description below sounds intriguing.
In numerical analysis, the ITP method, short for Interpolate Truncate and Project, is the first root-finding algorithm that achieves the superlinear convergence of the secant method[1] while retaining the optimal[2] worst-case performance of the bisection method.[3] It is also the first method with guaranteed average performance strictly better than the bisection method under any continuous distribution.[3] In practice it performs better than traditional interpolation and hybrid based strategies (Brent's Method, Ridders, Illinois), since it not only converges super-linearly over well behaved functions but also guarantees fast performance under ill-behaved functions where interpolations fail.[3]

Uses Bairstow's algorithm, code for dm42 and a PDF document. A matlab version is mentioned.

Polynomial root finder for {dm,hp}42s using Laguerre's method. Found on https://forum.swissmicros.com/viewtopic.php?p=20091#p20091
The Emacs tools for {dm,hp}42 code on https://richmit.github.io/hp42/hp42s-meta.html and the
Lisp library http://www.mitchr.me/SS/mjrcalc/ look interesting too.

mpmath is a free (BSD licensed) Python library for real and complex floating-point arithmetic with arbitrary precision. It has been developed by Fredrik Johansson since 2007, with help from many contributors.

Implementations in Basic and C.

Collection of FFT and related algorithm implementation in various programming languages.

Apart from the blog, there are technical notes https://www.johndcook.com/blog/writing/ and on-line calculators https://www.johndcook.com/blog/online-calculators/
As an example, see Camp-Paulson normal approximation to the binomial distribution https://www.johndcook.com/blog/camp_paulson/
The articles https://www.johndcook.com/blog/2024/04/01/more-laguerre-images/ and
https://www.johndcook.com/blog/2024/03/22/laguerres-root-finding-method/ demonstrate the basins of attraction for Laguerre's root-finding method.
https://www.johndcook.com/blog/2018/11/24/spheroid-distance/ should be useful for azel.
https://www.johndcook.com/blog/2020/02/08/arenstorf-orbit/ shows a periodic solution to the restricted 3-body problem.
https://www.johndcook.com/blog/2022/11/14/simultaneous-root-finding/ describes the Durand-Kerner polynomial root finding method.
https://www.johndcook.com/blog/2022/11/01/kepler-newton/ discusses solving Kepler's equation

TODO: https://www.johndcook.com/blog/2022/10/30/arctan-k-tan-t/ states "This plot looks similar to the plot of true anomaly for a highly elliptical orbit. I’m sure they’re related, but I haven’t worked out exactly how."

https://www.johndcook.com/blog/2022/10/21/math-origins/ explains V.I. Arnolds comment
"All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines), and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA)."

https://www.johndcook.com/blog/2018/09/24/riemann-hypothesis-the-fine-structure-constant-and-the-todd-function/ is about  Sir Michael Atiyah's incorrect proof of Riemann's hypothesis, the article https://rjlipton.com/2018/09/26/reading-into-atiyahs-proof/ is an interesting read. (I had bookmarked this entry on Wed Sep 26 15:51:47 2018 and put it here 2024-04-03.)

The article https://www.johndcook.com/non_central_chi_square.pdf sounds interesting:
John D. Cook Upper bounds on non-central chi-squared tails and truncated normal moments (2010). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 62.
Abstract. We show that moments of the truncated normal distribution provide upper bounds on the tails of the non-central chi-squared distribution, then develop upper bounds for the former.

Transcription of “The Great Debate”:
John Gustafson vs. William Kahan on Unum Arithmetic
Held July 12, 2016