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

To find out the coefficients of each of the different approximations, I have analytically written down and numerically solved them in MATLAB. I have used the Matrix inversion method to get the coefficients.

I have derived the required approximations using the Taylor Table method and used the coefficients received from the process as mentioned earlier to practice in the equations obtained by the Taylor table method.

By the plots generated, Central Differencing shows the least error when compared with Forward and Backward Differencing methods.

But, in few of the practical approaches, such as a boundary condition problem of uni-directional flow, Skewed scheme is a much better and a possible approach than a Central Difference scheme.