subject
to the condition
The
Euler formula is iterative. The iteration formulae are
A Level Maths Notes: FP3 – The Euler Formula for Numerical Solutions of First Order Differential Equations
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 formsubject
to the conditionThe
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.
