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Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions. (English) Zbl 1031.65080
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:
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L12Finite difference methods for ODE (numerical methods)
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory