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

Author:

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

Reference:

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:

boundary_locus.m, displays the region of absolute stability.

boundary_locus_test.m, calls all the tests.
boundary_locus_test.sh, runs all the tests.
boundary_locus_test.txt, the output file.

Stability region plots:

Last modified on 22 February 2021.