OOF2: The Manual
Name
Forward Euler (ForwardEuler) — Fully explicit first order time stepping.
Synopsis
ForwardEuler
()
Description
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
(i.e.
Field
values in OOF2) at
time ,
and the first order differential equation
the Forward Euler estimate for is
where .
ForwardEuler
can be applied to equations
with second order time derivatives
by defining new variables
and solving the augmented set of first order equations
ForwardEuler
works equally well for linear
and nonlinear equations. Because the method is explicit, equation
(6.138) doesn't require a nonlinear
solver even if is nonlinear.