[6.38] [math] Add test and improve doxygen of finite difference methods#22841
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[6.38] [math] Add test and improve doxygen of finite difference methods#22841root-project-bot wants to merge 5 commits into
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(cherry picked from commit 2cebd26)
The standard second-order central, backward and forward differences contained a mistake: a factor-of-4 error. See finite different coefficients here: https://en.wikipedia.org/wiki/Finite_difference_coefficient (cherry picked from commit 99c7a96)
Use a polynomial and its known derivatives to check the correctness of the finite difference methods. (cherry picked from commit 9851599)
(cherry picked from commit f715d64)
The test failed without any consequences because it was always returning 0. Other "tests" in this file will need to be updated to check their outputs in the future. Furthermore: - The second derivatives are unstable with short, so remove it from the test. - The targets for the second derivatives were wrong by a factor 4; fix. - Due to rounding, finite differences on integers don't exactly hit the target. Allow a delta of 1. (cherry picked from commit f3d03cb)
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July 17, 2026 09:48
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Backport of #22823, requested by @hageboeck.