Suppose we would like to approximate df/dx at x0 up to O(x 2 ) using function values

Suppose we would like to approximate df/dx at x0 up to O(Δx²) using function values at x₀,x₀ − Δx and x − 2Δx, that is,

 where α−₂,α−₁ and α₀ are unknown coefficients to be determined. Show that these coefficients are obtained by solving

Transcribed Image Text:

df dx = a−2f(xo-2x)+a_1f(xo-Ax) + of (x0) + O(△x²), XO