trapezoidal


trapezoidal, an R code which implements the (implicit) trapezoidal method for solving an ordinary differential equation (ODE), using fsolve() to handle the implicit equation, adapted from the pracma library of Hans Borchers.

Licensing:

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

Languages:

trapezoidal is available in a FreeFem++ version and a MATLAB version and an Octave version and a Python version and an R version.

Related Data and Programs:

adamsbashforth, an R code which uses an Adams Bashforth method to solve an ordinary differential equation (ODE).

backward_euler, an R code which implements the (implicit) backward Euler method for solving an ordinary differential equation (ODE), based on functions from the pracma library of Hans Borchers.

euler, an R code which uses the forward Euler method to solve a single ordinary differential equation (ODE).

eulersys, an R code which uses the forward Euler method to solve a system of ordinary differential equations (ODE).

midpoint, an R code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, solving the implicit equation using fsolve() from the pracma library of Hans Borchers.

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

rk4, an R code which uses a 4-th order Runge-Kutta method to solve an ordinary differential equation (ODE).

trapezoidal_test

trapezoidal_fixed, an R code which implements the (implicit) trapezoidal method for solving an ordinary differential equation (ODE), using a fixed point method to handle the implicit equation, adapted from the pracma library of Hans Borchers.

Author:

Adapted from original R code "cranknic()" by Hans Borchers for the pracma library; Modifications by John Burkardt.

Reference:

  1. Hans Borchers,
    package 'pracma'.

Source Code:


Last revised on 26 April 2021.