quadex_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.

Licensing:

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

Languages:

quadex_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 (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, an Octave code which defines the ordinary differential equations (ODE) for a Kepler two body gravitational problem.

kepler_perturbed_ode, an Octave code which defines the ordinary differential equations (ODE) for a perturbed Kepler two body gravitational problem.

lorenz_ode, an Octave code which approximates solutions to the Lorenz system of ordinary differential equations (ODE), which exhibit sensitive dependence on the initial conditions.

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_test

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 sets up and solves the Roessler ordinary differential equations (ODE) which exhibit 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 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, an Octave 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, an Octave code which defines the right hand side of the van der Pol oscillator ordinary differential equation (ODE).

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.

References:

  1. Charles Curtiss, Joseph Hirschfelder,
    Integration of Stiff Equations,
    Proceedings of the National Academy of Science, USA,
    Volume 38, Number 3, pages 235-243, March 1952.

Source Code:


Last revised on 19 October 2020.