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

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

**rk12** is available in
a MATLAB version and
an Octave version.

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

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

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

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

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

midpoint_fixed, a MATLAB 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.

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

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

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

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

rkf45, a MATLAB 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 MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method.

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

trapezoidal_fixed, a MATLAB 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.

- rk1.m implements a Runge Kutta method of order 1.
- rk12.m implements Runge Kutta methods of order 1 and 2.
- rk2.m implements a Runge Kutta method of order 2.