From: Wolfgang Bangerth <bangerth@math.tamu.edu>
Date: Wed, 30 Mar 2016 21:03:34 +0000 (-0500)
Subject: Fix signs of various terms.
X-Git-Tag: v8.5.0-rc1~1152^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=86a0c54779ff59aa099b970863e47795e5c20cf9;p=dealii.git

Fix signs of various terms.

This appears to be correct in the implementation, however.
---

diff --git a/examples/step-25/doc/intro.dox b/examples/step-25/doc/intro.dox
index 2921259f3d..92bfdd7bb8 100644
--- a/examples/step-25/doc/intro.dox
+++ b/examples/step-25/doc/intro.dox
@@ -109,7 +109,7 @@ sine-Gordon equation under consideration here, we have that
   F(u^n_l) &=&  \left[ 1-k^2\theta^2\Delta \right] u^n_l -  
                  \left[ 1+k^2\theta(1-\theta)\Delta\right] u^{n-1} - k v^{n-1} 
                  + k^2\theta\sin\left[\theta u^n_l + (1-\theta) u^{n-1}\right],\\
-  F'(u^n_l) &=& 1-k^2\theta^2\Delta - k^2\theta^2\cos\left[\theta u^n_l 
+  F'(u^n_l) &=& 1-k^2\theta^2\Delta + k^2\theta^2\cos\left[\theta u^n_l 
                         + (1-\theta) u^{n-1}\right].
 \f}
 Notice that while $F(u^n_l)$ is a function, $F'(u^n_l)$ is an operator.
@@ -153,13 +153,13 @@ H^1(\Omega)$. Thus, the finite-dimensional version of the variational formulatio
         U^{n,l+1} = U^{n,l} + \delta U^{n,l}, \qquad U^{n,0} = U^{n-1}; \\
   MV^n &=& MV^{n-1} - k \theta AU^n -k (1-\theta) AU^{n-1} - k S(u^n,u^{n-1}).
 @f}
-Above, the matrix $F_h'(\cdot)$ and the vector $F_h(\cdot)$ denote the discrete versions of the gadgets discussed above, i.e.
+Above, the matrix $F_h'(\cdot)$ and the vector $F_h(\cdot)$ denote the discrete versions of the gadgets discussed above, i.e.,
 \f{eqnarray*}
   F_h(U^{n,l}) &=&  \left[ M+k^2\theta^2A \right] U^{n,l} -  
                 \left[ M-k^2\theta(1-\theta)A \right] U^{n-1} - k MV^{n-1} 
                 + k^2\theta S(u^n_l, u^{n-1}),\\
   F_h'(U^{n,l}) &=& M+k^2\theta^2A 
-                                - k^2\theta^2N(u^n_l,u^{n-1})
+                                + k^2\theta^2N(u^n_l,u^{n-1})
 \f}
 Again, note that the first matrix equation above is, in fact, the
 definition of an iterative procedure, so it is solved multiple times
@@ -177,7 +177,7 @@ What solvers can we use for the first equation? Let's look at the matrix we
 have to invert:
 @f[
   (M+k^2\theta^2(A-N))_{ij} = 
-  \int_\Omega (1-k^2\theta^2 \cos \alpha) 
+  \int_\Omega (1+k^2\theta^2 \cos \alpha) 
   \varphi_i\varphi_j \; dx+\int_\Omega \nabla\varphi_i\nabla\varphi_j \; dx,
 @f]
 for some $\alpha$ that depends on the present and previous solution. First,
diff --git a/examples/step-25/step-25.cc b/examples/step-25/step-25.cc
index cf76f0efc8..9ce719834d 100644
--- a/examples/step-25/step-25.cc
+++ b/examples/step-25/step-25.cc
@@ -1,6 +1,6 @@
 /* ---------------------------------------------------------------------
  *
- * Copyright (C) 2006 - 2015 by the deal.II authors
+ * Copyright (C) 2006 - 2016 by the deal.II authors
  *
  * This file is part of the deal.II library.
  *
@@ -397,7 +397,7 @@ namespace Step25
   // @sect4{SineGordonProblem::compute_nl_term}
 
   // This function computes the vector $S(\cdot,\cdot)$, which appears in the
-  // nonlinear term in the both equations of the split formulation. This
+  // nonlinear term in both equations of the split formulation. This
   // function not only simplifies the repeated computation of this term, but
   // it is also a fundamental part of the nonlinear iterative solver that we
   // use when the time stepping is implicit (i.e. $\theta\ne 0$). Moreover, we