Exercise $2($python code required$)$

Interpolation and numerical derivation

Let the following points be :

Handwrite the table of divided differences to calculate independence.

Determine numerically

$(h=0\mathrm{.}1).$ Start first with the value of $y1$ from the previous question to hand$-$calculate the $y3$

iteration of the prediction$-$correction method.

Plot the exact solution and the numerical approximations obtained with the two

methods. Calculate the maximum relative error common to each method. Indicate and comment

on the results obtained. With Python, Spyder.