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Zbl 1031.65080
Simos, T.E.; Famelis, I.T.; Tsitouras, C.
Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions. (English)
[J] Numer. Algorithms 34, No.1, 27-40 (2003). ISSN 1017-1398; ISSN 1572-9265/e

Summary: New explicit, zero dissipative, hybrid Numerov type methods are presented. We derive these methods using an alternative which avoids the use of costly high accuracy interpolatory nodes. We only need the Taylor expansion at some internal points then. The method is of sixth algebraic order at a cost of seven stages per step while their phase lag order is fourteen. The zero dissipation condition is satisfied, so the methods possess an non empty interval of periodicity. Numerical results over some well known problems in physics and mechanics indicate the superiority of the new method.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65L12 Finite difference methods for ODE
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: initial value problems (IVP); numerical results; hybrid Numerov methods; phase-lag; oscillating solutions

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