flame_ode, a Python code which considers an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
flame_ode is available in a MATLAB version and an Octave version and a Python version.
arenstorf_ode, a Python code which describes an ordinary differential equation (ODE) which defines a stable periodic orbit of a spacecraft around the Earth and the Moon.
biochemical_linear_ode, a Python code which defines a linear biochemical ordinary differential equation (ODE).
biochemical_nonlinear_ode, a Python code which defines a nonlinear biochemical ordinary differential equation (ODE).
blowup_ode, a Python code which considers an ordinary differential equation (ODE) y'=y^2. whose solution "blows up" in finite time.
brusselator_ode, a Python code which defines the Brusselator ordinary differential equation (ODE) system.
dosage_ode, a Python code which uses a system of ordinary differential equations (ODE) to simulate the blood levels of a medicinal drug that should stay between medicinal and toxic limits.
exp_ode, a Python code which sets up an ordinary differential equation (ODE) whose solution is an exponential function.
henon_heiles_ode, a Python code which solves the Henon-Heiles system of ordinary differential equations (ODE) which model the motion of a star around the galactic center.
humps_ode, a Python code which solves an ordinary differential equation (ODE) whose solution is a double hump curve.
kepler_ode, a Python code which defines the ordinary differential equations (ODE) for a Kepler two body gravitational problem.
kepler_perturbed_ode, a Python code which defines the ordinary differential equations (ODE) for a perturbed Kepler two body gravitational problem.
lorenz_ode, a Python code which approximates solutions to the Lorenz system of ordinary differential equations (ODE), which exhibit sensitive dependence on the initial conditions.
normal_ode, a Python code which sets up an ordinary differential equation (ODE) for the normal probability density function (PDF).
oscillator_ode, a Python code which defines the highly oscillatory ordinary differential equation (ODE).
pendulum_double_ode, a Python code which defines the double pendulum ordinary differential equation (ODE).
pendulum_nonlinear_ode, a Python code which sets up the ordinary differential equations (ODE) that represent a nonlinear model of the behavior of a pendulum of length L under a gravitational force of strength G.
pendulum_ode, a Python code which sets up the ordinary differential equations (ODE) that represent a linear model of the behavior of a pendulum of length L under a gravitational force of strength G.
predator_prey_ode, a Python code which solves a pair of predator prey ordinary differential equations (ODE).
quadex_ode, a Python code which solves a stiff ordinary differential equation (ODE), whose exact solution is a parabola, but for which errors grow exponentially.
quasiperiodic_ode, a Python code which sets up a system of ordinary differential equations (ODE) for a problem with a quasiperiodic solution.
rigid_body_ode, a Python code which solves the ordinary differential equations (ODE) representing the Euler equations for a rigid body with three unequal moments of inertia, originally proposed by Fred Krogh.
ripple_ode a Python code which solves an ordinary differential equation (ODE) whose family of solutions start as ripples and end as hyperbolas.
robertson_ode, a Python code which sets up a system of three nonlinear stiff ordinary differential equations (ODE) characterizing an autocatalytic chemical reaction.
roessler_ode, a Python code which sets up and solves the Roessler ordinary differential equations (ODE) which exhibit chaotic behavior.
rubber_band_ode, a Python code which defines and solves a set of ordinary differential equations (ODE) describing a mass suspended by a spring and rubber band, which can exhibit chaotic behavior.
sir_ode, a Python code which sets up the ordinary differential equations (ODE) which simulate the spread of a disease using the Susceptible/Infected/Recovered (SIR) model.
stiff_ode, a Python code which considers an ordinary differential equation (ODE) which is an example of a stiff ODE.
three_body_ode, a Python code which defines a set of ordinary differential equations (ODE) which simulates the behavior of three planets, constrained to lie in a plane, and moving under the influence of gravity, by Walter Gander and Jiri Hrebicek.
two_body_ode, a Python code which defines ordinary differential equations (ODE) which simulate the behavior of two bodies, constrained to lie in a plane, moving under the influence of gravity, with one body much more massive than the other.
vanderpol_ode, a Python code which defines the right hand side of the van der Pol oscillator ordinary differential equation (ODE).
zombie_ode, a Python code which sets up a system of ordinary differential equations (ODE) for a generalized SIR infection model to simulate a zombie attack, developed by Philip Munz.