A symbolic-numerical package for linear stability analysis
of numerical methods for ODEs
                        by
          M.Cafaro (*), B.Paternoster (**)
(*) Faculty of Engineering, University of Lecce,
    Palazzo Stecca, Via per Monteroni, 73100 Lecce, Italy,
    e-mail: cafaro@sara.unile.it

(**) Dipartimento di Matematica e Informatica, 
     Universita' di Salerno,
     Via S. Allende, 84081 Baronissi (Salerno), Italy,
     e-mail: beapat@dia.unisa.it
             na.paternoster@na-net.ornl.gov
     84081 Baronissi (Salerno)
 
In recent years we have been considering the possibility of using
symbolic computation in the analysis and development of new numerical
methods for Ordinary Differential Equations (ODEs), looking at computer
algebra from the point of view of its users.
We present the Mathematica package StabInt.m which computes the intervals of
stability of rational functions, when they are regarderd as stability
functions of numerical methods for ODEs. The package is very flexible
because it ignores the form of the method under analysis, considering
the inequalities which represent the stability  conditions.
The possibility to perform the computation with different accuracies allows
the user to detect ill-conditioned situations.
The package is freely available on http://www.netlib.org/ode/symbolic.