new

[book_gpu.git] / BookGPU / Chapters / chapter16 / bdf.tex

diff --git a/BookGPU/Chapters/chapter16/bdf.tex b/BookGPU/Chapters/chapter16/bdf.tex
index bd4e5d5364b881f3044336428d7c82c7cfa959ac..6035b0b3744f0cde1ee5bddcbd6f7dec87945c2a 100644 (file)
--- a/BookGPU/Chapters/chapter16/bdf.tex
+++ b/BookGPU/Chapters/chapter16/bdf.tex
@@ -34,7 +34,7 @@ the index $i$ in $h_i$, $\alpha_1^i$ and $\alpha_2^i$ can be omitted.
 
 For the first step $t_1$,
 only the initial condition at $t_0$ is available.
 
 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{equation}\label{eq:BE}
    \tfrac{1}{h_1}[q(x_1)-q(x_0)] + f(x_1) = b_1.
 \end{equation}


@@ -117,8 +117,8 @@ J\! =\! \frac{\ud x_M}{\ud x_0}
 \end{equation}
 
 \begin{algorithm}
 \end{equation}
 
 \begin{algorithm}

-\caption{The matrix-free\index{matrix-free} method for
- Krylov subspace\index{Krylov subspace} construction.}
+\caption{the matrix-free\index{matrix-free} method for
+ Krylov subspace\index{iterative method!Krylov subspace} construction}

 \label{alg:mf_Gear}
   \KwIn{ current Krylov subspace basis vector $v$,
            time step lengths $h_i$,
 \label{alg:mf_Gear}
   \KwIn{ current Krylov subspace basis vector $v$,
            time step lengths $h_i$,