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.


65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L12 Finite difference and finite volume methods for ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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