Finite Difference Coefficient Generation

finiteDifference.jl

order = 4
stencil = [-3 -2 -1 0 1]

S = zeros(Int64,order+1,length(stencil))
for i = 1:length(stencil)
    for j = 0:order
        S[j+1,i] = stencil[i] ^ j
    end
end

D = zeros(Int64,order+1)
D[order+1] = factorial(order)

C = S\D

x = range(0,2*pi,length=1000)
F = sin.(x)
DF = zeros(Float64,1000)
for i = 4:999
    DF[i] = sum((C .* F[i.+stencil]') ./ (x[2]-x[1])^order)
end