midpoint_explicit


midpoint_explicit, an Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also known as the modified Euler method.

Licensing:

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

Languages:

midpoint_explicit is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and an Octave version and a Python version and an R version

Related Data and codes:

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

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

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

midpoint_explicit_test

midpoint_fixed, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, solving the implicit equation with a fixed point method.

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

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

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

rk4, an Octave code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).

rk45, an Octave code which implements Runge-Kutta ODE solvers of orders 4 and 5.

rkf45, an Octave code which implements the Runge-Kutta-Fehlberg ODE solver.

trapezoidal, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and using fsolve to solve the implicit equation.

trapezoidal_fixed, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and using a fixed point method to solve the implicit equation.

Reference:

  1. Catalin Trenchea, John Burkardt,
    Refactorization of the midpoint rule,
    Applied Mathematics Letters,
    Volume 107, September 2020.

Source Code:


Last revised on 26 April 2021.