OOF2: The Manual
Backward Euler (BackwardEuler) — Fully implicit first order time stepping.
The Backward Euler method is a method of numerically integrating ordinary differential equations. Like the ForwardEuler method, it is first order in time, meaning that it makes an error of order on each step. It is more stable than the Forward Euler method, especially for diffusion equations, but requires more effort to compute. It is less accurate than CrankNicolson, but in some cases less prone to oscillations.
Given a vector of unknowns
Field values in OOF2) at
and the first order differential equation
the Backward Euler solution is given by solving
for , with . Because appears on the right hand side, this is an implicit method and is relatively costly to compute, especially when is nonlinear.
BackwardEuler can be applied to equations
with second order time derivatives via equation (6.141).