X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/17bff40b83bcdcc39769f9e59c70ffae1c525b72..ca38d6218b9ba6a0fd2e0b2126c6b38146504b8e:/BookGPU/Chapters/chapter16/ef.tex diff --git a/BookGPU/Chapters/chapter16/ef.tex b/BookGPU/Chapters/chapter16/ef.tex index 400b467..1cc747b 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],