Lotka-Volterra equation solver

This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to Lotka-Volterra equations: \[ \begin{aligned} \dfrac{dx}{dt} &= \alpha x - \beta xy \\ \dfrac{dy}{dt} &= \delta xy - \gamma y \end{aligned} \] where \(x\) is the number of prey animals and \(y\) is the number of predator animals and \(\alpha, \beta, \gamma\), and \(\delta\) describe their interactions with one another.

Parameter	Value	Explanation
\(\alpha\):		Interaction parameter.
\(\beta\):		Interaction parameter.
\(\gamma\):		Interaction parameter.
\(\delta\):		Interaction parameter.
\(t_0\):		Starting time for the simulation in seconds (s).
\(t_f\):		End time for the simulation in seconds.
\(x_0\):		Prey population.
\(y_0\):		Predator population.
\(\epsilon\):		Error tolerance in both \(x\) and \(y\). \(\epsilon \lt \)1e-7 often freezes the webpage with \(t_f \geq 100\).
dtInitial:		Initial guess for step size.