OOF2: The Manual
Forward Euler (ForwardEuler) — Fully explicit first order time stepping.
The Forward Euler method is the simplest method of numerically integrating ordinary differential equations. The individual steps are very quick to compute, but the method is often unstable, requiring very small step sizes. It is first order in time, meaning that it makes an error of order on each step.
Given a vector of unknowns
Field values in OOF2) at
and the first order differential equation
the Forward Euler estimate for is
ForwardEuler can be applied to equations
with second order time derivatives
by defining new variables
and solving the augmented set of first order equations