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 2921259f3d85ce6bbfb1d55e627ed54a7ba30e93..92bfdd7bb8a479a4cd83027517565cd8273275a1 100644 (file)
--- 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 cf76f0efc8a1ec4e877c52375f7fdd7d475e2678..9ce719834df5f748d72fa268045516c4c5cb4165 100644 (file)
--- 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