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A Runge-Kutta Fehlberg method with phase-lag of order infinity for initial-value problems with oscillating solution. (English) Zbl 0777.65046

Conventional Runge-Kutta-methods use small stepsize for the integration of equations describing free oscillations, in order to obtain accurate approximations along the intervals used. The author proposes methods suitable for a long interval integration step, not only when the oscillating equation is subject to free oscillations of high frequency, but also in the case of forced oscillations of low frequency.
One of the mentioned methods for the numerical solution of systems of ordinary differential equations of the form \(y'=f(x,y)\) is third order algebraic, has phase-lag of order infinitely, and is dissipative of order four. Numerical examples show, that these methods are much more accurate compared with other classical methods used in problems with oscillating equations.
Reviewer: H.Ade (Mainz)

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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