Lorenz equations solver

This webpage uses the Runge-Kutta-Fehlberg fourth-order method with fifth-order error checking (RKF45) to approximate the solution to Lorenz equations: \[ \begin{aligned} \dfrac{dx}{dt} &= \sigma (y-x) \\ \dfrac{dy}{dt} &= x (\rho - z) - y \\ \dfrac{dz}{dt} &= xy - \beta z. \end{aligned} \]

Parameter	Value	Explanation
\(\sigma\):		Problem parameter.
\(\rho\):		Problem parameter.
\(\beta\):		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.