kepler_perturbed_ode


kepler_perturbed_ode, an Octave code which considers an ordinary differential equation (ODE) which models a perturbed Kepler two-body gravitational problem.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

kepler_perturbed_ode is available in a MATLAB version and an Octave version.

Related Data and codes:

allen_cahn_ode, an Octave code which sets up and solves the 1D Allen-Cahn reaction-diffusion ordinary differential equation (ODE).

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.

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 (ODEs) 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, an Octave code which defines an ordinary differential equation (ODE) which models a Kepler two-body gravitational problem.

kepler_perturbed_ode_test

lorenz_ode, an Octave code which approximates solutions to the Lorenz system, creating output files that can be displayed by gnuplot.

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 (ODEs) 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 (ODEs) 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's).

quasiperiodic_ode, an Octave code which sets up a system of ordinary differential equations (ODEs) for a problem with a quasiperiodic solution.

rk12, an Octave code which implements Runge-Kutta ODE solvers of orders 1 and 2.

rk23, an Octave code which implements Runge-Kutta ODE solvers of orders 2 and 3.

rk34, an Octave code which implements Runge-Kutta ODE solvers of orders 3 and 4.

rk45, an Octave code which implements Runge-Kutta ODE solvers of orders 4 and 5.

rkf45, an Octave code which implements the Runge-Kutta-Fehlberg ODE solver.

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 (ODEs) 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)s 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)s which model motion on the surface of a sphere.

spring_ode, an Octave code which shows how line printer graphics can be used to make a crude illustration of a solution of the ordinary differential equation (ODE) that describes the motion of a weight attached to a spring.

spring_ode2, an Octave code which shows how gnuplot graphics can be used to illustrate a solution of the ordinary differential equation (ODE) that describes the motion of a weight attached to a spring.

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).

test_ode, an Octave code which defines ordinary differential equations (ODE) test problems.

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)s for a generalized SIR infection model to simulate a zombie attack, developed by Philip Munz.

References:

  1. Ernst Hairer, Christian Lubich, Gerhard Wanner,
    Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations,
    Springer, 2006,
    ISSN: 0179-3632.

Source Code:


Last revised on 03 August 2020.