explicit 15-stage Runge-Kutta methods of order 10

[ChrisRackauckas]

https://arxiv.org/abs/2504.17329

1. The representation "NUM" of the eq. (10) method from the text in its rounded decimal form (90 digits) in the following format: It is 15 rows for c, 15 rows for b, and 1 + 2 + 3 + ... + 14 = 105 rows for below the diagonal part of A, row by row.

2. Expressions for its "EXACT" values. Each row contains 9 integers which is representation of a number as explained on page 11 of the text --- first 8 integers divided by the 9th integer are the rational coefficients at 1, sqrt(3), sqrt(7), sqrt(21), alpha, beta, sqrt(7)*alpha, sqrt(7)*beta.

3. A program in Julia "ord_n.jl" which reads the numbers in "NUM" and checks the order conditions up to specified from the command line order p. One can run it as
   julia ord_n.jl 10 < NUM

4. A program in Julia "ord_e.jl" which reads the "EXACT" representation and checks the order conditions up to specified from the command line order p. One can run it as
   julia ord_e.jl 10 < EXACT

5. A file "trees.jl" that contains rooted trees related functions that "ord_n.jl" and "ord_e.jl" use.

fw15stagerkoforder10.zip