$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Requirements of a program
- Compute the numerical solution \( u^n \), \( n=1,2,\ldots,N_t \)
- Display the numerical and exact solution \( \uex(t)=e^{-at} \)
- Bring evidence to a correct implementation (verification)
- Compare the numerical and the exact solution in a plot
- computes the error \( \uex (t_n) - u^n \)
- computes the convergence rate of the numerical scheme
- reads its input data from the command line
