$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Test the understanding!
Derive Forward Euler, Backward Euler, and Crank-Nicolson schemes for
Newton's law of cooling:
$$ T' = -k(T-T_s),\quad T(0)=T_0,\ t\in (0,t_{\mbox{end}}]$$
Physical quantities:
- \( T(t) \): temperature of an object at time \( t \)
- \( k \): parameter expressing heat loss to the surroundings
- \( T_s \): temperature of the surroundings
- \( T_0 \): initial temperature
