boundary_locus

boundary_locus, a MATLAB code which uses the boundary locus method to display the region of absolute stability for an ODE solution method, based on a procedure by Randall Leveque.

The analysis begins by applying the ODE solution method to the model equation:

y' = lambda * y
then letting z represent the product h*lambda, where h is the stepsize, and reformulating the solution method as
Ynew = R(z) * Yold
The method will be absolutely stable if |R(z)| < 1. We can then simply create a contour plot of the function |R(z)| to display the stability region.

Licensing:

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

Languages:

boundary_locus is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

boundary_locus_test

boundary_locus2, a MATLAB code which uses the boundary locus method to display the border of the region of absolute stability for a solver of ordinary differential equations (ODE).

Author:

Original MATLAB coding by Randall Leveque. Modifications by John Burkardt.

Reference:

  1. Randall Leveque,
    Finite difference methods for ordinary and partial differential equations,
    Society for Industrial and Applied Mathematics, 2007,
    ISBN13: 978-0-898716-29-0.

Source Code:

Last modified on 22 February 2021.