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Extension to a variable coefficient; Forward and Backward Euler
\begin{equation}
u'(t) = -a(t)u(t),\quad t\in (0,T],\quad u(0)=I
\tag{32}
\end{equation}
The Forward Euler scheme:
\begin{equation}
\frac{u^{n+1} - u^n}{\Delta t} = -a(t_n)u^n
\end{equation}
The Backward Euler scheme:
\begin{equation}
\frac{u^{n} - u^{n-1}}{\Delta t} = -a(t_n)u^n
\end{equation}
