conservation_ode

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

In most real world cases, the exact solution of an ODE is not known. In many such cases, however, one or more conserved quantities can be identified, such as mass, momentum, or energy. Then an important indicator of ODE solution quality is the accuracy with which conservation constraints are observed.

ODE's which have a conserved quantity include:

• arenstorf_ode
• biochemical_linear_ode
• biochemical_nonlinear_ode
• double_well_ode
• henon_heiles_ode
• kepler_ode
• kepler_perturbed_ode
• oscillator_ode
• ozone_ode
• ozone2_ode
• pendulum_double_ode
• pendulum_elastic_ode
• pendulum_nonlinear_ode
• pendulum_ode
• predator_prey_ode
• reaction_ode
• reaction_twoway_ode
• rigid_body_ode
• robertson_ode
• sir_ode
• spring_ode
• squircle_ode
• zombie_ode

Licensing:

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

Languages:

conservation_ode is available in a MATLAB version and an Octave version and aPython version..

Related Data and Programs:

conservation_ode_test

matlab_ode, MATLAB codes which set up various ordinary differential equations (ODE).

Reference:

• Lawrence Shampine,
  Conservation laws and the numerical solution of ODEs,
  Computers and Mathematics with Applications,
  Volume 12B, Number 5-6, pages 1287-1296, 1986.

Source code:

The pendulum.

• pendulum_conserved.m, evaluates a quantity that should be conserved for the ODE.
• pendulum_deriv.m, returns the right hand side of the ODE.
• pendulum_parameters.m, returns parameters of the ODE.

Predator prey.

• predator_prey_conserved.m, evaluates a conserved quantity.
• predator_prey_deriv.m, defines the right hand side of the ODE.
• predator_prey_parameters.m, returns the parameter values of the ODE.

Rigid body.

• rigid_body_conserved.m, evaluates a conserved quantity for the ODE.
• rigid_body_deriv.m, returns the right hand side of the ODE.
• rigid_body_parameters.m, returns parameter values for the ODE.