boundary_locus, a Python 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 * ythen letting z represent the product h*lambda, where h is the stepsize, and reformulating the solution method as
Ynew = R(z) * YoldThe 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.
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
boundary_locus is available in a MATLAB version and an Octave version and a Python version.
boundary_locus2, a Python 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).
MATLAB version by Randall Leveque. Python version by John Burkardt.