**python_ode**,
Python codes which
sets up ordinary differential equations (ODE).

arenstorf_ode, a Python code which sets up an ordinary differential equation (ODE) which defines a stable periodic orbit of a spacecraft around the Earth and the Moon.

axon_ode, a Python code which sets up the ordinary differential equations (ODE) for the Hodgkin-Huxley model of an axon.

biochemical_linear_ode, a Python code which sets up a linear biochemical ordinary differential equation (ODE).

biochemical_nonlinear_ode, a Python code which sets up a nonlinear biochemical ordinary differential equation (ODE).

blood_pressure_ode, a Python code which sets up and solves an ordinary differential equation (ODE) which models the variation in blood pressure in the human artery.

blowup_ode, a Python code which sets up an ordinary differential equation (ODE) y'=y^2. whose solution "blows up" in finite time.

brusselator_ode, a Python code which sets up the Brusselator ordinary differential equation (ODE) system.

conservation_ode, a Python code which monitors the conservation of a quantity that should be constant, during the solution of an ordinary differential equation (ODE).

dosage_ode, a Python code which sets up a system of ordinary differential equations (ODE) to simulate the blood levels of a medicinal drug that should stay between medicinal and toxic limits.

duffing_ode, a Python code which sets up a second-order ordinary differential equation (ODE) whose solution can exhibit chaotic behavior.

exp_ode, a Python code which sets up an ordinary differential equation (ODE) whose solution is an exponential function.

fitzhugh_nagumo_ode, a Python code which sets up the Fitzhugh-Nagumo system of ordinary differential equations (ODE).

flame_ode, a Python code which sets up an ordinary differential equation (ODE) that models the growth of a ball of flame in a combustion process.

glycolysis_ode, a Python code which sets up a pair of ordinary differential equations (ODE) that model the biochemical process of glycolysis, for which a limit cycle exists.

grazing_ode, a Python code which sets up a pair of ordinary differential equations (ODE) that model the populations of an edible plant, and the herbivore that grazes on it.

heartbeat_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) describing the beating of the heart, as suggested by Zeeman.

henon_heiles_ode, a Python code which sets up 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 sets up an ordinary differential equation (ODE) whose solution is a double hump curve.

kepler_ode, a Python code which sets up the ordinary differential equations (ODE) for a Kepler two body gravitational problem.

kepler_perturbed_ode, a Python code which sets up the ordinary differential equations (ODE) for a perturbed Kepler two body gravitational problem.

lindberg_ode, a Python code which sets up a system of 4 ordinary differential equations (ODE) which are very stiff.

logistic_ode, a Python code which sets up and solves an ordinary differential equation (ODE) which models population growth in the face of a limited carrying capacity.

lorenz_ode, a Python code which sets up 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 sets up the highly oscillatory ordinary differential equation (ODE).

ozone_ode, a Python code which sets up a stiff system of four ordinary differential equations (ODE) that simulate the daily variation in atmospheric ozone concentration.

ozone2_ode, a Python code which sets up a stiff system of four ordinary differential equations (ODE) that simulate the daily variation in atmospheric ozone concentration. This version of the ozone ODE includes a nitrogen oxide source term.

pendulum_double_ode, a Python code which sets up the double pendulum ordinary differential equation (ODE).

pendulum_elastic_ode a Python code which sets up the ordinary differential equations (ODE) that represent the behavior of a nonlinear elastic pendulum, with gravitational force G, spring constant K, unstretched length L, and mass M.

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.

polar_ode, a Python code which sets up an ordinary differential equation (ODE) whose variable is complex, and whose solution should be viewed in a polar coordinate plot.

predator_prey_ode, a Python code which sets up a pair of predator prey ordinary differential equations (ODE).

quadex_ode, a Python code which sets up 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.

reaction_ode, a Python code which sets up the ordinary differential equations (ODE) which model a simple chemical reaction A+B --k--> C.

reaction_twoway_ode, a Python code which sets up the ordinary differential equations (ODE) which model a two-way chemical reaction between species W1 and W2.

rigid_body_ode, a Python code which sets up 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 sets up 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 sets up ordinary differential equations (ODE) describing a mass suspended by a spring and rubber band, which can exhibit chaotic behavior.

sawtooth_ode, a Python code which sets up an ordinary differential equation (ODE) driven by a right hand side which is a sawtooth function (periodic, discontinuous, piecewise linear).

sensitive_ode, a Python code which sets up a second order ordinary differential equation (ODE) which exhibits sensitive dependence on the initial condition.

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.

sling_ode, a Python code which sets up ordinary differential equations (ODE) for which the exact circular solution can only be approximated for a short interval before it decays to zero.

spring_ode, a Python code which sets up ordinary differential equations (ODE) for the motion of a spring with mass m, damping b, and stiffness k.

spring_double_ode, a Python code which sets up ordinary differential equations (ODE) for a system in which a mass is connected by a spring to a mass connected by a spring to a fixed support.

spring_sweep_ode, a Python code which computes a grid of solutions to a parameterized system of ordinary differential equations (ODE) that represent the motion of a spring with mass m, damping b, and stiffness k.

squircle_ode, a Python code which sets up a system of ordinary differential equations (ODE) for a pair of functions that generalize the sine and cosine, and whose phase portrait is a squircle (a sort of squared circle).

stetter_ode, a Python code which sets up an ordinary differential equation (ODE) for which a specific time step sequence causes the implicit trapezoid rule to be unstable, while the implicit midpoint rule will be stable. Note that the right hand side function f(t,y) is periodic, discontinuous, and piecewise linear.

stiff_ode, a Python code which sets up an ordinary differential equation (ODE) which exhibits stiffness, making accurate solution difficult.

three_body_ode, a Python code which sets up 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.

tough_ode, a Python code which sets up four ordinary differential equations (ODE) which is extremely difficult to solve accurately.

two_body_ode, a Python code which sets up 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.

unstable_ode, a Python code which sets up an unstable ordinary differential equation (ODE) which the backward Euler method incorrectly drives to zero.

vanderpol_ode, a Python code which sets up the van der Pol oscillator ordinary differential equation (ODE).

zombie_ode, a Python code which sets up ordinary differential equations (ODE) for a generalized SIR infection model to simulate a zombie attack, developed by Philip Munz.