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Added Butcher's Fifth Order Runge-Kutta Algorithm - Matched and Updated RK4 implementation #3148

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@digitalvirtuoso digitalvirtuoso commented Oct 10, 2020

Describe your change:

Addressing #2510

Added Butcher's Fifth Order Runge-Kutta Method.

Followed the same code formatting, comments, and doctest as was in the original Runge-Kutta (RK4) implementation. Updated Existing Runge-Kutta Fourth Order method and comments to make both formulas easier to read for someone wanting to investigate the wikipedia and learn more about these numerical analysis methods.

  • [X ] Added an algorithm
  • [X ] Documentation change / Updated existing code

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All functions have doctests that pass the automated testing.
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@digitalvirtuoso digitalvirtuoso commented Oct 12, 2020

Can a reviewer kindly review this for Hacktoberfest? Glad to help and add an additional algorithm, feedback is welcome! :)

@digitalvirtuoso digitalvirtuoso changed the title Hacktoberfest - Added Butcher's Fifth Order Runge-Kutta Algorithm - Matched and Updated RK4 implementation Added Butcher's Fifth Order Runge-Kutta Algorithm - Matched and Updated RK4 implementation Oct 18, 2020
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