**rk45**,
a Python code which
implements Runge-Kutta ODE solvers of orders 4 and 5.

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

**rk45** is available in
a MATLAB version and
an Octave version and
a Python version.

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euler, a Python code which solves one or more ordinary differential equations (ODEs) 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 (ODEs) 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 ODE solvers of orders 1 and 2.

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

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

rk4, a Python code which implements a fourth-order Runge-Kutta-Fehlberg ODE solver.

rkf45, a Python code which implements the Runge-Kutta-Fehlberg ODE solver.

test_ode, a Python code which defines some sample ODE's for testing initial value problem solvers;

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.

- predator_rk4_phase.png a phase plot produced by predator_rk4().
- predator_rk5_phase.png a phase plot produced by predator_rk5().
- predator_rk4_plot.png a solution plot produced by predator_rk4().
- predator_rk5_plot.png a solution plot produced by predator_rk5().