3.6. Time stepping

Until now, we just used partial_t() to express time derivatives. However, the particular time stepping method in numerical simulations is of utmost importance for accurate results, which is even more the case if e.g. energy should be conserved. Therefore, this section is dedicated to the time stepping within pyoomph. Second order time derivatives are always calculated with the Newmark-beta method of second order (called "Newmark2" in the following), which is exactly the same time stepping which is used in oomph-lib. First order derivatives can be either calculated with the implicit (or backward) Euler method, which is first order accurate. Since this method coincides with the backward differentiation formula (BDF) of first order, it will be called "BDF1" in the following. The BDF of second order for first derivatives is also implemented, which is called "BDF2". In fact "BDF2" is the default method for first order time derivatives in pyoomph.