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.