X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/17bff40b83bcdcc39769f9e59c70ffae1c525b72..6318153555fcb28c475d77850cce474032d79f5a:/BookGPU/Chapters/chapter5/ch5.tex?ds=sidebyside diff --git a/BookGPU/Chapters/chapter5/ch5.tex b/BookGPU/Chapters/chapter5/ch5.tex index f780577..bdfad6a 100644 --- a/BookGPU/Chapters/chapter5/ch5.tex +++ b/BookGPU/Chapters/chapter5/ch5.tex @@ -188,7 +188,7 @@ We use a Method of Lines (MoL)\index{method of lines} approach to solve \eqref{c \begin{align}\label{ch5:eq:discreteheateq} \frac{\partial u}{\partial t} = \mymat{A}\myvec{u}, \qquad \mymat{A} \in \mathbb{R}^{N\times N}, \quad \myvec{u} \in \mathbb{R}^{N}, \end{align} -where $\mymat{A}$ is the sparse finite difference matrix and $N$ is the number of unknowns in the discrete system. The temporal derivative is now free to be approximated by any suitable choice of a time-integration method\index{time integration}. The most simple integration scheme would be the first-order accurate explicit forward Euler method\index{forward Euler}, +where $\mymat{A}$ is the sparse finite difference matrix and $N$ is the number of unknowns in the discrete system. The temporal derivative is now free to be approximated by any suitable choice of a time-integration method\index{time integration}. The most simple integration scheme would be the first-order accurate explicit forward Euler method\index{Euler!forward Euler}, \begin{align}\label{ch5:eq:forwardeuler} \myvec{u}^{n+1} = \myvec{u}^n + \delta t\,\mymat{A}\myvec{u}^n, \end{align}