From 90c16c6e64e40464c0aee5b051b2352896121e04 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Fri, 7 Jan 2022 03:41:31 -0700 Subject: [PATCH] Fix symbol confusion in step-52. --- examples/step-52/doc/intro.dox | 7 ++++--- examples/step-52/step-52.cc | 4 ++-- 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/examples/step-52/doc/intro.dox b/examples/step-52/doc/intro.dox index 4f4caf45bd..ee1e081444 100644 --- a/examples/step-52/doc/intro.dox +++ b/examples/step-52/doc/intro.dox @@ -110,10 +110,10 @@ y_{n+1} = y_n + \sum_{i=1}^s b_i k_i @f} where for the form of the right hand side above @f{eqnarray*} -k_i = h M^{-1} f\left(t_n+c_ih,y_n+\sum_{j=1}^sa_{ij}k_j\right). +k_i = \Delta t \, M^{-1} f\left(t_n+c_ih,y_n+\sum_{j=1}^sa_{ij}k_j\right). @f} Here $a_{ij}$, $b_i$, and $c_i$ are known coefficients that identify which -particular Runge-Kutta scheme you want to use, and $h=t_{n+1}-t_n$ is the time step +particular Runge-Kutta scheme you want to use, and $\Delta t=t_{n+1}-t_n$ is the time step used. Different time stepping methods of the Runge-Kutta class differ in the number of stages $s$ and the values they use for the coefficients $a_{ij}$, $b_i$, and $c_i$ but are otherwise easy to implement since one can look up @@ -135,7 +135,8 @@ $a_{ii}\neq 0$ for at least one of the stages $i=1,\ldots,s$. Many well known time stepping schemes that one does not typically associate with the names Runge or Kutta can in fact be written in a way so that they, too, can be expressed in these categories. They oftentimes represent the -lowest-order members of these families. +lowest-order members of these families; one example is the simple explicit +Euler method.

Explicit Runge-Kutta methods

diff --git a/examples/step-52/step-52.cc b/examples/step-52/step-52.cc index 49a02de71b..5256e347ff 100644 --- a/examples/step-52/step-52.cc +++ b/examples/step-52/step-52.cc @@ -662,8 +662,8 @@ namespace Step52 // @sect4{Diffusion::run} // // The following is the main function of the program. At the top, we create - // the grid (a [0,5]x[0,5] square) and refine it four times to get a mesh - // that has 16 by 16 cells, for a total of 256. We then set the boundary + // the grid (a $[0,5]\times [0,5]$ square) and refine it four times to get a + // mesh that has 16 by 16 cells, for a total of 256. We then set the boundary // indicator to 1 for those parts of the boundary where $x=0$ and $x=5$. void Diffusion::run() { -- 2.39.5