Duffing JavaScript integrator

This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to the problem of the Duffing oscillator:

\ddot{x} + \delta \dot{x} + \alpha x + \beta x^3 = \gamma \cos{(\omega t)}

Below you can specify these various parameters, as well as the initial conditions and starting and end times. The default values give chaotic behaviour.

Parameter	Value	Explanation
$\alpha$ :		Parameter.
$\beta$ :		Parameter.
$\gamma$ :		Parameter.
$\delta$ :		Parameter.
$\omega$ :		Parameter.
$t_0$ :		Starting time for the simulation in seconds (s).
$t_f$ :		End time for the simulation in seconds..
$x_0$ :		x coordinate (in metres) at time $t_0$ .
$\dot{x}_0$ :		First derivative of $x$ with respect to $t$ at $t_0$ (in $\mathrm{metres}\cdot \mathrm{s}^{-1}$ ).
$\epsilon$ :		Error tolerance in both $\theta$ and $\dot{\theta}$ . $\epsilon \lt$ 2e-12 often freezes the webpage.
dtInitial:		Initial guess for step size.