The Euler (forward) formula is the simplest numerical method for estimating values of a function at a point. It can be applied to any problem of the form
subject to the condition
The Euler formula is iterative. The iteration formulae are
Similar backwards iteration formulae exist.
The Euler formula is one of the least accurate numerical methods. It is useful for small values of
and
but errors increase rapidly as these increase in magnitude.
Example: If
with
use Euler's formula to estimate
with
This simple problem can be solved exactly by separation of variables.
