X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/17bff40b83bcdcc39769f9e59c70ffae1c525b72..55ce7168c6e69a2462d76c95dc9a5298ceedb04f:/BookGPU/Chapters/chapter16/ef.tex diff --git a/BookGPU/Chapters/chapter16/ef.tex b/BookGPU/Chapters/chapter16/ef.tex index 400b467..812c97a 100644 --- a/BookGPU/Chapters/chapter16/ef.tex +++ b/BookGPU/Chapters/chapter16/ef.tex @@ -52,7 +52,7 @@ significant savings in simulation time. % One simple way to estimate $x((m+k)T)$ is to use the information at % $mT$ and $(m-1)T$, which leads to the forward-Euler method as To estimate $x((m+k)T)$, -a forward Euler\index{forward Euler} style jumping relies only on $x(mT)$ and $x((m-1)T)$, +a forward Euler\index{Euler!forward Euler} style jumping relies only on $x(mT)$ and $x((m-1)T)$, i.e., \[ x((m+k)T) @@ -61,7 +61,7 @@ i.e., \] However, this approach is inefficient due to its restriction on envelope step $k$, since larger $k$ usually causes instability. -Instead, backward Euler\index{backward Euler} jumping, +Instead, backward Euler\index{Euler!backward Euler} jumping, %and the equation becomes \[ x((m+k)T)-x(mT) = k\left[x((m+k)T)-x((m+k-1)T)\right], @@ -133,7 +133,7 @@ In summary, the envelope-following method is fundamentally a boosted version of traditional transient analysis, with certain skips over several periods and a Newton iteration to update or correct the errors brought by the skips, -as is exhibited by Fig.~\ref{fig:ef_flow}. +as is exhibited by Figure~\ref{fig:ef_flow}. \begin{figure}[!tb] \centering \resizebox{.7\textwidth}{!}{\input{./Chapters/chapter16/figures/ef_flow.pdf_t}}