In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.

Why do we use Euler's method?

Euler's method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can't be solved using a more traditional method, like the methods we use to solve separable, exact, or linear differential equations.

How do you calculate Euler's equation?

The basic approach to solving Euler equations is similar to the approach used to solve constant-coefficient equations: assume a particular form for the solution with one constant “to be determined”, plug that form into the differential equation, simplify and solve the resulting equation for the constant, and then ...