We here use one of the simpler time stepping methods, namely the second order
in time Crank-Nicolson method. This is surely already better than the even
-more widely used (and even less accurate) implicit Euler method,
-but many other, more accurate methods such as
+more widely used (and even less accurate) implicit (=backward) Euler method,
+but many other, more accurate methods such as BDF or
Runge-Kutta methods are available and should be used as they do not represent
much additional effort. It is not difficult to implement this for the current
program, if one wanted; a more systematic treatment is also given in step-52.
Rather, one should use one of the available
high-quality libraries for time stepping, for the same reasons as one should
not be implementing finite element methods by hand but use deal.II instead.
-Indeed, deal.II has interfaces to one such time stepping library,
-[SUNDIALS](https://computing.llnl.gov/projects/sundials), already available.
+Indeed, deal.II has interfaces to two such time stepping library,
+[SUNDIALS](https://computing.llnl.gov/projects/sundials) and the
+[PETSc TS package](https://petsc.org/release/manualpages/TS/TS/), already available.
In particular, the SUNDIALS::ARKode class would make for a great starting
-point for the use of much better (and much more accurate) time steppers;
+point for the use of much better (and much more accurate) time steppers,
+as would PETScWrappers::TimeStepper;
the methods one would then get also implement the automatic time step
-control mentioned above.
+control mentioned above. To see how this works, take a look at
+step-86.
<h4>Better refinement criteria</h4>
/**
* Interface to the PETSc TS solver for Ordinary Differential Equations
* and Differential-Algebraic Equations. The TS solver is described in the
- * [PETSc manual](https://petsc.org/release/manual/ts/).
+ * [PETSc manual](https://petsc.org/release/manual/ts/). This class is used
+ * and extensively discussed in step-86.
*
* This class supports two kinds of formulations.
* The explicit formulation: