fdm_demo.jl

#+BEGIN_SRC jupyter-julia
using Interpolations
xs = range(-10, 10, length=50) # 50 evenly spaced points from -5 to 5

# model function, some Gaussian
f(x; A=1, σ=2, b=0) = A * exp(-x^2/2σ) + b
ys = f.(xs)

method = BSpline(Cubic(Line(OnGrid()))) #interpolation method
f_itp = scale(interpolate(ys, method), xs) # interpolation function

using FiniteDifferences: fdm, central_fdm

fdm(central_fdm(5, 1), f_itp, 1.0, Val(true))

#+END_SRC

#+RESULTS:
: (FiniteDifferenceMethod:
:   order of method:       5
:   order of derivative:   1
:   grid:                  -2:2
:   coefficients:          [0.08333333333333333, -0.6666666666666666, 0.0, 0.6666666666666666, -0.08333333333333333]
:   roundoff error:        1.42e-14
:   bounds on derivatives: 6.89e-02
:   step size:             4.25e-03
:   accuracy:              6.26e-12
: , -0.3892357438391503)