From 9f954ae0afb3b285b10a4f8463f8f6fc55396f56 Mon Sep 17 00:00:00 2001 From: Bruno Turcksin Date: Fri, 16 May 2014 19:04:54 +0000 Subject: [PATCH] Fix typos in the documentation of step-52. git-svn-id: https://svn.dealii.org/trunk@32927 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-52/doc/intro.dox | 6 +++--- deal.II/examples/step-52/step-52.cc | 8 ++++---- 2 files changed, 7 insertions(+), 7 deletions(-) diff --git a/deal.II/examples/step-52/doc/intro.dox b/deal.II/examples/step-52/doc/intro.dox index 4ae88a593d..11d19584c0 100644 --- a/deal.II/examples/step-52/doc/intro.dox +++ b/deal.II/examples/step-52/doc/intro.dox @@ -8,7 +8,7 @@ This program shows how to use Runge-Kutta methods to solve a time-dependent problem. -

Problem statement

+

Problem statement

In this example, we solve the energy-integrated time-dependent diffusion approximation of the neutron transport equation (see step-28 for the @@ -36,7 +36,7 @@ S=A\left(\frac{1}{v}\omega \cos(\omega t)(bx -x^2) + \sin(\omega t) \left(\Sigma_a (bx-x^2)+2D\right) \right). @f} Because the solution is a sine, we know that -\f$\phi\left(x,\frac{\pi}{\omega}\right) = 0$. Therefore, we can easily +$\phi\left(x,\frac{\pi}{\omega}\right) = 0$. Therefore, we can easily compute the error at this time since it is simply the norm of the solution found. @@ -74,7 +74,7 @@ categories:

Explicit Runge-Kutta

These methods that include for forward Euler, third order Runge-Kutta, and -fourth order Runge-Kutta, require a function to evaluate $M^{-1}f(t,y). These +fourth order Runge-Kutta, require a function to evaluate $M^{-1}f(t,y)$. These methods become unstable when the time step chosen is too large.

Embedded Runge-Kutta

diff --git a/deal.II/examples/step-52/step-52.cc b/deal.II/examples/step-52/step-52.cc index 1031e49cdd..f13222ed70 100644 --- a/deal.II/examples/step-52/step-52.cc +++ b/deal.II/examples/step-52/step-52.cc @@ -83,11 +83,11 @@ namespace Step52 // Compute the intensity of the source at the given point. double get_source(double time,const Point<2> &point) const; - // Evaluate the diffusion equation \f$M^{-1}(f(t,y))\f$ + // Evaluate the diffusion equation $M^{-1}(f(t,y))$ Vector evaluate_diffusion(const double time, const Vector &y) const; - // Evaluate \f$\left(I-\tau M^{-1} \frac{\partial f(t,y)}{\partial y}\right)^{-1} = - // \left(M-\tau \frac{\partial f}{\partial y}\right)^{-1} M \f$ + // Evaluate $\left(I-\tau M^{-1} \frac{\partial f(t,y)}{\partial y}\right)^{-1} = + // \left(M-\tau \frac{\partial f}{\partial y}\right)^{-1} M $ Vector id_minus_tau_J_inverse(const double time, const double tau, const Vector &y); @@ -196,7 +196,7 @@ namespace Step52 cell = dof_handler.begin_active(), endc = dof_handler.end(); - // Compute \f$-\int D \nabla b \cdot \nabla b - \int \Sigma_a b b\f$ and \f$\int b b\f$ + // Compute $-\int D \nabla b \cdot \nabla b - \int \Sigma_a b b $ and $\int b b $ for (; cell!=endc; ++cell) { cell_matrix = 0.; -- 2.39.5