* truncation of the Taylor scheme; dual numbers do not contain any higher-order terms in their first derivative,
* while for the complex-step method these existent higher-order terms are neglected. It can be shown that
* both of these methods are not subject to subtractive cancellation errors and that, within their
- * finite-difference scheme, they are not numerically sensitive to the internal step-size chosen for the
+ * finite-difference scheme, they are not numerically sensitive to the internal \step-size chosen for the
* numerical perturbation. The dual number approach thus produces exact first derivatives, while the
* complex-step approximation does not. The standard implementation of the dual numbers, however, cannot yield
* exact values for second derivatives. Hyper-dual numbers take a different view of this idea, with numbers
<ol>
<li> <p> New:
- The step-19 tutorial demonstrates handling of parameters from a
+ The \step-19 tutorial demonstrates handling of parameters from a
parameter file, as well as some simple techniques for merging output
from parallel computations.
<br>
<li> <p>
New: If there are references to other example programs in any of the
- step-XX programs, then they will now show up as crosslinks in the HTML
+ \step-XX programs, then they will now show up as crosslinks in the HTML
version for simpler navigation of the tutorial.
<br>
(WB, 2005/04/04)
<li> <p>
Extended: The <code>ParameterHandler</code> class now does a much better
job generating output in the <code>print_parameters()</code> function if
- parameters have documentation strings attached to them. See the step-19
+ parameters have documentation strings attached to them. See the \step-19
example program output for this.
<br>
(WB, 2005/09/12)
-<h3>\Step-13 revisited</h3>
+<h3>step-13 revisited</h3>
If instead of the <code>Exercise_2_3</code> data set, we choose
// The task to be performed by the next three functions is to calculate a
// mass matrix and a Laplace matrix on the temperature system. These will be
// combined in order to yield the semi-implicit time stepping matrix that
- // consists of the mass matrix plus a time step-dependent weight factor
+ // consists of the mass matrix plus a time \step-dependent weight factor
// times the Laplace matrix. This function is again essentially the body of
// the loop over all cells from step-31.
//
// In the function that runs the WorkStream for actually calculating the
// right hand side, we also generate the final matrix. As mentioned above,
// it is a sum of the mass matrix and the Laplace matrix, times some time
- // step-dependent weight. This weight is specified by the BDF-2 time
+ // \step-dependent weight. This weight is specified by the BDF-2 time
// integration scheme, see the introduction in step-31. What is new in this
// tutorial program (in addition to the use of MPI parallelization and the
// WorkStream class), is that we now precompute the temperature
//
// This function will provide us with an initial guess by using a
// continuation method as we discussed in the introduction. The Reynolds
- // number is increased step-by-step until we reach the target value. By
+ // number is increased \step-by-step until we reach the target value. By
// experiment, the solution to Stokes is good enough to be the initial guess
// of NSE with Reynolds number 1000 so we start there. To make sure the
// solution from previous problem is close enough to the next one, the step
// <code>U</code> and a time point <code>t</code> (as input arguments)
// computes the updated solution, stores it in the vector
// <code>temp</code>, swaps its contents with the vector <code>U</code>,
- // and returns the chosen step-size $\tau$.
+ // and returns the chosen \step-size $\tau$.
//
// The other important method is <code>prepare()</code> which primarily
// sets the proper partition and sparsity pattern for the temporary
// The big changes in this program are in the creation of matrix and right
// hand side, since they are problem-dependent. We will go through that
- // process step-by-step, since it is a bit more complicated than in previous
+ // process \step-by-step, since it is a bit more complicated than in previous
// examples.
//
// The first parts of this function are the same as before, however: setting