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

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


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
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