rk23, a MATLAB code which implements Runge-Kutta solvers of orders 2 and 3 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.
rk23 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.
rk12, a MATLAB code which implements Runge-Kutta solvers of orders 1 and 2 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.