Deriving fourth order approximation of second order derivative with skewed schemes

Objective:

The objective is to derive fourth order approximation of skewed right side , left side & central scheme with the help of taylor's table & numerical stencil.

The equation one will be

`del^2f`/`delx^2` -------- (1)

Stencil that we are using for this fourth order approximation is

Based on the stencil the PDE can be re-write as

`del^2f`/`delx^2``approx` af(i) + bf(i+1) + cf(i+2) + df(i+3) +ef(i+4)

The above equation is second order PDE from that we are compute the fourth order approximation of