From: Wolfgang Bangerth <bangerth@colostate.edu>
Date: Fri, 7 Jan 2022 10:41:31 +0000 (-0700)
Subject: Fix symbol confusion in step-52.
X-Git-Tag: v9.4.0-rc1~654^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=90c16c6e64e40464c0aee5b051b2352896121e04;p=dealii.git

Fix symbol confusion in step-52.
---

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.
 
 
 <h4>Explicit Runge-Kutta methods</h4>
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{<code>Diffusion::run</code>}
   //
   // 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()
   {