Euler's method

Euler’s method is an algorithm that lets us numerically approximate the solutions to a differential equation, assuming we are given some initial-value problem.

We compute this iteratively based on previous calculations. Where $h$ is some step length:

$$x_{n+1}=x_n+h$$ $$y_{n+1}=y_n+hf(x_n,y_n)$$

This is premised on the idea of linear approximations. The smaller the step size, the smaller the error (and the more accurate the approximation). The further away our initial point, the worse our approximation is.