Week 3.5 - Deriving 4th order approximation of a 2nd order derivative using Taylor Table method

AIM:
Aim of the project is to derive the 4th order approximation of the second-order derivative using central difference, Skewed right-sided difference, Skewed left-sided difference.

Taylor Table:
Tylor table is the collection of Tylor series representation. By using taylor table we can come up with numerical schemes to meet the target accuracy. Consider the below example, I need to come up with 2nd order accurate approximation. I need to do that by using points i, i+1 and i+2.

Mathlab Coding:

The main program which computes all three function

Second-order derivative by Right difference scheme

Second-order derivative by Left difference scheme

Second-order derivative by Central difference scheme

Figure: