Lorenz 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}

This system were first derived by Edward Lorenz and colleagues as a simplified mathematical model of atmospheric convection, although it can also arise in other fields. It is frequently used as an example of chaotic systems.

Simulation parameter form.
Parameter	Value	Explanation
$\sigma$ :		Problem parameter
$\rho$ :		Problem parameter
$\beta$ :		Problem parameter
$t_f$ :		End time for the simulation in seconds (s)
$x_0$ :		Initial $x$ coordinate.
$y_0$ :		Initial $y$ coordinate.
$z_0$ :		Initial $z$ coordinate.
$\epsilon$ :		Error tolerance.
$\mathrm{Tol}_{\mathrm{type}}$ :		Tolerance type, can be either absolute (0) or relative (1).
$h_{\mathrm{Initial}}$ :		Initial step size.
$h_{\mathrm{Min}}$ :		Minimum allowed step size.
$\Delta t$ :		Time increment for skipping ahead in animation.
$t_1$ :		Time you want to skip ahead to in animation when you press the skip button.
$\mathrm{Width}$ :		Width (in px) of Plotly windows used for plotting and animation below.
$\mathrm{Height}$ :		Height (in px) of Plotly windows used for plotting and animation below.
$t_\mathrm{Scale}$ :		Proportion of animation time passed per real time. $t_{\mathrm{Scale}}=1.0$ means animation and real time match. $t_{\mathrm{Scale}}<1.0$ means the animation is going more slowly than real time. $t_{\mathrm{Scale}}>1.0$ means it is going more rapidly.

© Brenton Horne. I do not claim to be infallible, so feel free to open issues or pull requests on GitHub if you notice flaws or things that can be improved.
I favour Oxford spelling, so if you notice I generally use different spelling to Australian spelling, that is probably why.
Homepage. Source code: https://github.com/fusion809/fusion809.github.io.
Website built with Franklin.jl.

Lorenz solver

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