https://www.wikiwand.com/en/Euler_method

For a first-order Initial value problem

$y_{i+1}=y_i+hf(x,y)$

where $h$ is the time step. It's like the left-hand approximation of the integral, at each step.

The Modified Euler method approximates the trapezium rule.

Truncation error $O(h^2)$