## 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 ofandbut errors increase rapidly as these increase in magnitude.

Example: Ifwithuse Euler's formula to estimatewith

This simple problem can be solved exactly by separation of variables.