midpoint_fixed, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, with a simple fixed-point iteration to solve the implicit equation.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
midpoint_fixed is available in a MATLAB version.
backward_euler, a MATLAB code which solves one or more ordinary differential equations (ODE) using the backward Euler method.
backward_euler_fixed, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using a fixed point iteration for the implicit equation.
cauchy_method, a MATLAB code which solves one or more ordinary differential equations (ODE) using the Cauchy 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.
rk12, a MATLAB code which implements Runge-Kutta solvers of orders 1 and 2 for a system of ordinary differential equations (ODE).
rk23, a MATLAB code which implements Runge-Kutta ODE solvers of orders 2 and 3.
rk34, a MATLAB code which implements Runge-Kutta ODE solvers of orders 3 and 4.
rk4, a MATLAB code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).
rk45, a MATLAB code which implements Runge-Kutta ODE solvers of orders 4 and 5.
rkf45, a MATLAB code which implements the Runge-Kutta-Fehlberg ODE solver.
theta_method, a MATLAB code which solves one or more ordinary differential equations (ODE) using the theta method.
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.
velocity_verlet, a MATLAB code which uses a version of the velocity Verlet method to solve a secord order ordinary differential equation (ODE) of the form y''=f(t,y).