For the first step $t_1$,
only the initial condition at $t_0$ is available.
-Therefore backward-Euler is used, i.e.,
+Therefore backward Euler is used, i.e.,
\begin{equation}\label{eq:BE}
\tfrac{1}{h_1}[q(x_1)-q(x_0)] + f(x_1) = b_1.
\end{equation}
\begin{algorithm}
\caption{The matrix-free\index{matrix-free} method for
- Krylov subspace\index{Krylov subspace} construction.}
+ Krylov subspace\index{iterative method!Krylov subspace} construction.}
\label{alg:mf_Gear}
\KwIn{ current Krylov subspace basis vector $v$,
time step lengths $h_i$,