midpoint_adaptive

midpoint_adaptive, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, relying on fsolve() to solve the implicit equation, and using an adaptive timestep. Plots of the solution and timestep history are created.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

midpoint_adaptive is available in a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and codes:

midpoint_adaptive_test

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midpoint, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, relying on fsolve() to solve the implicit equation, and using a fixed time step.

midpoint_explicit, an Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method, and using a fixed time step.

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trapezoidal, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and using a fixed time step.

trapezoidal_explicit, an Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) trapezoidal method, and using a fixed time step.

trapezoidal_fixed, an Octave 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, and using a fixed time step.

velocity_verlet, an Octave 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).

Reference:

  1. William Milne,
    Numerical Integration of Ordinary Differential Equations,
    American Mathematical Monthly,
    Volume 33, number 9, pages 455–460, 1926.
  2. Ernst Hairer, Syvert Norsett, Gerhard Wanner,
    Solving ordinary differential equations, I. Nonstiff problems,
    Springer Series in Computational Mathematics, Number 8,
    Springer-Verlag, Berlin, 1987.
  3. Catalin Trenchea, John Burkardt,
    Refactorization of the midpoint rule,
    Applied Mathematics Letters,
    Volume 107, September 2020.

Source Code:


Last revised on 23 February 2022.