Using Lagrange interpolation, fit a quadratic polynomial p ( x ), to node points x j ˆ’ 1 , x j ,x j +1 . This takes the form
hence
and so evaluating this derivative at node x j we have:
Hence we fine the polynomial S j , j = 0, 1, , n ˆ’ 2 such that:
This gives rise to coefficient values defined by (see [ 20 ]):