arenstorf_ode, an Octave code which describes an ordinary differential equation (ODE) which defines a stable periodic orbit of a spacecraft around the Earth and the Moon.
Although the orbit should be periodic, and repeats after a time interval of a little more than 17 units, most ODE solvers will have difficulty coming close to periodicity.
The computer code and data files described and made available on this web page are distributed under the MIT license
arenstorf_ode is available in a MATLAB version and an Octave version and a Python version.
biochemical_linear_ode, an Octave code which defines a linear biochemical ordinary differential equation (ODE).
biochemical_nonlinear_ode, an Octave code which defines a nonlinear biochemical ordinary differential equation (ODE).
brusselator_ode, an Octave code which defines the Brusselator ordinary differential equation (ODE) system.
double_pendulum_ode, an Octave code which defines the double pendulum ordinary differential equation (ODE).
flame_ode, an Octave code which considers an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process.
henon_heiles_ode, an Octave 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, an Octave code which solves an ordinary differential equation (ODE) whose solution is a double hump curve.
kepler_ode_test an Octave code which considers an ordinary differential equation (ODE) which models a Kepler two-body gravitational problem.
kepler_perturbed_ode an Octave code which considers an ordinary differential equation (ODE) which models a perturbed Kepler two-body gravitational problem.
lorenz_ode, an Octave code which approximates solutions to the Lorenz system, creating output files that can be displayed by gnuplot.
normal_ode, an Octave code which sets up an ordinary differential equation (ODE) for the normal probability density function (PDF).
oscillator_ode, an Octave code which defines the highly oscillatory ordinary differential equation (ODE).
pendulum_nonlinear_ode, an Octave code which sets up the ordinary differential equations (ODE) that represent a nonlinear model ofthe behavior of a pendulum of length L under a gravitational force of strength G.
pendulum_ode, an Octave code which sets up the ordinary differential equations (ODE) that represent a linear model ofthe behavior of a pendulum of length L under a gravitational force of strength G.
predator_prey_ode, an Octave code which solves a pair of predator prey ordinary differential equations (ODE).
quadex_ode, an Octave code which solves a stiff ordinary differential equation (ODE), whose exact solution is a parabola, but for which errors grow exponentially.
quasiperiodic_ode, an Octave code which sets up a system of ordinary differential equations (ODE) for a problem with a quasiperiodic solution.
robertson_ode, an Octave code which sets up a system of three nonlinear stiff ordinary differential equations (ODE) characterizing an autocatalytic chemical reaction.
roessler_ode, an Octave code which defines the right hand side of the Roessler ODE system, which exhibits chaotic behavior.
rubber_band_ode, an Octave 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, an Octave code which sets up the ordinary differential equations (ODE) which simulate the spread of a disease using the Susceptible/Infected/Recovered (SIR) model.
sphere_ode, an Octave code which sets up the ordinary differential equations (ODE) which model motion on the surface of a sphere.
stiff_ode, an Octave code which considers an ordinary differential equation (ODE) which is an example of a stiff ODE.
string_ode, an Octave code which simulates the behavior of a vibrating string by solving the corresponding initial boundary value problem (IBVP).
three_body_ode, an Octave code 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, an Octave code which simulates 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.
zombie_ode, an Octave 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.