https://github.com/ocramz/rungekutta

https://github.com/ocramz/rungekutta

Last synced: 3 months ago
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• Host: GitHub
• URL: https://github.com/ocramz/rungekutta
• Owner: ocramz
• License: other
• Created: 2022-03-09T17:49:50.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2022-03-10T15:18:56.000Z (over 3 years ago)
• Last Synced: 2025-07-08T20:23:31.846Z (3 months ago)
• Language: Haskell
• Size: 16.6 KB
• Stars: 1
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README
  • License: LICENSE

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README

          
This is a small module collecting about a dozen Runge-Kutta methods

of different orders, along with a couple of programs to exercise them.

Build and run testrk, volterra, volterra2, and arenstorf:

o   testrk exercises all of the methods in a non-adaptive way,

    solving a test problem with a known analytic solution,

    to check convergence. (This was what first indicated that

    there was a problem with the Fehlberg 7(8) listing in HNW.)

o   volterra uses a non-adaptive method to solve the Lotka-Volterra

    equations from t=0 to t=40: either from a built-in starting point,

    or from a starting point specified on the command line.

o   volterra2 does the same, except it uses an adaptive solver

o   arenstorf solves the restricted 3-body problem (earth+moon+satellite)

    using an adaptive solver with some specific initial conditions

    which yield periodic orbits

The volterra2 and arenstorf examples use an "oracle" function to

decide what is a good step size. Right now that oracle function is in

each test file; arguably it should be in the RungeKutta module.

Eventually it will be, but I haven't spent much time yet on making

that oracle especially good.