Rework derivative discretizations - Githubissues

alexfikl / pycaputo

Evaluate fractional integrals and solve fractional ODEs.

https://pycaputo.readthedocs.io

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Rework derivative discretizations #57

Closed alexfikl closed 1 month ago

alexfikl commented 2 months ago

See discussion in #55. Methods that need updating

Caputo

[x] L1
[x] ModifiedL1
[x] L2
[ ] L2C
[ ] SpectralJacobi
- This method evaluates the derivative on the whole grid.
[ ] YuanAgrawal
- These diffusive methods do not have weights in the sense from #55. However, we can still implement evaluating at a given point.
[ ] Diethelm
[ ] BirkSong

Riemann-Liouville

Should just work once Caputo methods are updated.

Grünwald-Letnikov

[ ] GrunwaldLetnikov
[ ] ShiftedGrunwaldLetnikov
[ ] TianZhouDeng2
[ ] TianZhouDeng3

Gradient

Reimplement gradient based on diffs method. Methods that don't support it can take a long hard look at themselves.

Fixes #55.

alexfikl commented 1 month ago

This turned out to be a bit of a pain. Had to re-derive most of the methods to be able to write out the weights and diffs separately.

For now, the interface seems nice enough and the most used methods are ported. The rest of them can be done one by one whenever someone finds the time and the will :grin: