Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions. (English) Zbl 0624.65058

Van der Houwen, P. J.; Sommeijer, B. P.

SIAM J. Numer. Anal. 24, 595-617 (1987).

Explicit Runge-Kutta-Nyström (RKN) methods are constructed for numerical integration of vector ODE’s \(d^ ky/dt^ k=f(t,y)\); \(k=1,2\), having an oscillatory solution. The methods are designed so as for linear systems (with \(f(t,y)=Ay+g(t))\) the phase error of the free oscillations be small. Thus the integration step may be chosen much larger than the step required by the standard RKN methods. Another class of problems considered have solutions that consist of free oscillations of high frequency and forced oscillations of low frequency. Since the methods are explicit they are suitable for ODE’s that are not stiff.

Reviewer: V.A.Velev

MSC:

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
34A30	Linear ordinary differential equations and systems

Keywords:

periodic solutions; non-stiff systems; explicit Runge-Kutta-Nyström methods; oscillatory solution; linear systems; phase error; free oscillations; forced oscillations