Analysis of stability of rational approximations through computer algebra

We present a Mathematica package to compute the interval of stability of one or more rational approximations for mathematical functions. This analysis has a strong connection with the linear stability theory of numerical methods for Ordinary Differential Equations. As an example of the application of this package, we analyze the periodicity properties of Padè approximations for the cosine function. Moreover, we show its usefulness in the derivation of new numerical methods, by applying it to maximize the periodicity interval of collocation--based methods for second order initial value problems

Analysis of Stability of Rational Approximations through computer algebra

We present a Mathematica package to compute the interval of stability of one or more rational approximations for mathematical functions. This analysis has a strong connection with the linear stability theory of numerical methods for Ordinary Differential Equations. As an example of the application of this package, we analyze the periodicity properties of Pade approximations for the cosine function. Moreover, we show its usefulness in the derivation of new numerical methods, by applying it to maximize the periodicity interval of collocation-based methods for second order initial value problems