Rabinovich–Fabrikant equations solver

This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to Rabinovich–Fabrikant equations: \[ \begin{aligned} \dfrac{dx}{dt} &= y(z-1+x^2) + \gamma x \\ \dfrac{dy}{dt} &= x (3z+1-x^2) + \gamma y \\ \dfrac{dz}{dt} &= -2z(\alpha+xy). \end{aligned} \]

Parameter	Value	Explanation
\(\alpha\):		Problem parameter.
\(\gamma\):		Problem parameter.
\(t_0\):		Starting time for the simulation in seconds (s).
\(t_f\):		End time for the simulation in seconds.
\(x_0\):		Value of \(x\) at \(t_0\).
\(y_0\):		Value of \(y\) at \(t_0\).
\(z_0\):		Value of \(z\) at \(t_0\).
\(\epsilon\):		Error tolerance. \(\epsilon \lt\) 1.8e-10 usually freezes the webpage up.
dtInitial:		Initial guess for step size.