Forward Euler Integration / Euler
Usage
The desired integration method used for continuous-time dynamics is passed to the simulate
function as a keyword argument.
using SimpleSim
# my_model = ...
out = simulate(my_model, T = T_end, integrator = Euler)
Mathematical Background
The state $x^+$ estimating the true state at time $t+\Delta t$ is determined by simple integration of the current derivative $\dot{x}(t)$ computed using the dynamics function $f(x(t), u(t), p, t)$.
\[x^+ = x + \Delta t \cdot f(x, u(t), p, t)\]
This method is also referred to as forward Euler method and is the most basic explicit method for solving initial value problems.
You can read more about this topic on Wikipedia or any text book on the topic, many of which are available on the internet.
Performance
For each iteration, the dynamics function $f$ is only called once and the state update itself is computationally very inexpensive.