Compuation of the interval of stability of Runge-Kutta-Nyström methods. (English) Zbl 0908.65071

Paternoster, B.; Cafaro, M.

J. Symb. Comput. 25, No. 3, 383-394 (1998).

The interval of stability of a Runge-Kutta-Nyström method is the largest interval \((-\beta ,0)\) such that for all \(\lambda h^2\in (-\beta ,0)\) the method, applied with step size \(h\) to \(y''-\lambda y =0\), gives a bounded solution. This article presents a ‘Mathematica’ package which, for a given Runge-Kutta-Nyström method, computes the interval of stability.

Reviewer: E.Hairer (Genève)

MSC:

65L20	Stability and convergence of numerical methods for ordinary differential equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems
68W30	Symbolic computation and algebraic computation

Keywords:

Runge-Kutta-Nyström methods; stability interval; symbolic computation; Mathematica package

Software:

Mathematica