Free(OnGrid()) boundary conditions produce surprising results about interpolations.jl

[mkitti]

You've encountered https://en.wikipedia.org/wiki/Runge%27s_phenomenon

[CChapmanbird]

I have never seen such a bad case of it for not-a-knot cubic splines - especially for such a simple function. The true curve appears almost linear at the boundary but the cubic polynomial is totally different...

I suppose more nodes is the only answer?

[mkitti]

Perhaps. The reality is that you probably only need more nodes near the boundaries.

true curve appears almost linear at the boundary

Have you tried Natural?

Also consider
https://github.com/jipolanco/BSplineKit.jl
https://github.com/JuliaApproximation/ApproxFun.jl

[CChapmanbird]

Thanks for the recommendations - I did not know about BSplineKit.jl.

I thought that Line is an alias for Natural? In the docs....

"The following boundary conditions are implemented: Flat, Line (alternatively, Natural), Free, Periodic and Reflect."