Interesting catalog of methods for numerical methods for ODEs

[Valentin Albillo]

(10-23-2019 09:11 PM)JMBaillard Wrote:  Here is a link to programs I've just written to solve ODEs with a 10th-order Runge-Kutta method:

http://hp41programs.yolasite.com/rk10.php

Following your link I've seen that you're using a 17-stage (k1, k2, ..., k17) RK10 method needing 169 constants in all.

I'm curious: Why haven't you used instead a 16-stage RK10 method ? (same order but only 136 constants in all)

It would run significantly faster (1 stage less and fewer constants as well), would use less memory registers (33 data registers would be saved, as well as many program registers while initializing the constants) and the precision would be about the same or better.

V.