rk23

rk23, a Python code which implements Runge-Kutta solvers of orders 2 and 3 for a system of ordinary differential equations (ODE).

Licensing:

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

Languages:

rk23 is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

backward_euler, a Python code which solves one or more ordinary differential equations (ODE) using the backward Euler method.

euler, a Python code which solves one or more ordinary differential equations (ODE) using the forward Euler method.

leapfrog, a Python code which uses the leapfrog method to solve a second order ordinary differential equation (ODE) of the form y''=f(t,y).

midpoint, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.

midpoint_explicit, a Python code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.

midpoint_fixed, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, using a simple fixed-point iteration to solve the implicit equation.

rk12, a Python code which implements Runge-Kutta solvers of orders 1 and 2 for a system of ordinary differential equations (ODE).

rk34, a Python code which implements Runge-Kutta solvers of orders 3 and 4 for a system of ordinary differential equations (ODE).

rk4, a Python code which implements a fourth-order Runge-Kutta-Fehlberg solver for a system of ordinary differential equations (ODE).

rk45, a Python code which implements Runge-Kutta solvers of orders 4 and 5 for a system of ordinary differential equations (ODE).

rkf45, a Python code which implements the Runge-Kutta-Fehlberg solvers of orders 4 and 5 for the adaptive solution of a system of ordinary differential equations (ODE).

trapezoidal, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method.

trapezoidal_explicit, a Python code which solves one or more ordinary differential equations (ODE) using the (explicit) trapezoidal method.

trapezoidal_fixed, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, using the fixed point method to handle the implicit system.

Source Code:

• rk23.py the source code.
• rk23.sh runs all the tests.
• rk23.txt the output file.

• predator_rk2_phase.png a phase plot produced by predator_rk2().
• predator_rk3_phase.png a phase plot produced by predator_rk3().
• predator_rk2_plot.png a solution plot produced by predator_rk2().
• predator_rk3_plot.png a solution plot produced by predator_rk3().