Fully parallel Runge-Kutta-Nyström methods for ODEs with oscillating solutions. (English) Zbl 0782.65090

Crisci, M. R.; Paternoster, B.; Russo, E.

Appl. Numer. Math. 11, No. 1-3, 143-158 (1993).

This paper deals with Runge-Kutta-Nyström methods, whose coefficient matrix \(A\) is diagonal. Indeed the algebraic order of these methods is at most two or three but the dispersive order is increasing with the stage number and the methods still remain \(P\)-stable. Two- and three-stage methods are constructed which are very useful in integrating oscillatory problems. Numerical tests are given.

Reviewer: R.Scherer (Karlsruhe)

MSC:

65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65Y05	Parallel numerical computation
65L05	Numerical methods for initial value problems involving ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

\(P\)-stability; multi stage method; parallel computation; Runge-Kutta- Nyström methods; algebraic order; dispersive order; oscillatory problems; Numerical tests

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