Numerical Analysis. Coding portions must be written in Python.

Initial Value Problems Higher$-$Order

$($a$)$ Derive the Explicit Trapezoid Rule for solving an Initial Value Problem given by:

$Y=y_i+hf(t_i,y_i)$

$y_{i+1}=y_i+\frac{h}{2}(f(t_i,y_i)+f(t_{i+1},Y))$

$($b$)$ Using the Explicit Trapezoid Rule, compute the first $3$ steps, in other words $y_1,y_2,$ and $y_3,$

for the solution of the IVP given in $(2)$ using $h=0\mathrm{.}2.$ You may implement a python code or

do this by hand.