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

According to the images of the derived schemes attached, we see that they are fourth order accurate due to the term Δx^4 appearing as the highest order term which denotes the equations order from it's exponent "4".

When viewing the provided plot, it can be seen that the central differencing method yields more accurate results due to the significantly lower error. However, it is not always possible to use the central differencing method. For instance, in the case of determining numerical approximations for a function at the boundary node, central differencing cannot be used because both sides of the node are needed. This is where a skewed scheme can make up for what the central scheme cannot accomplish because a skewed scheme needs only one side to compute the solution.