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Zbl 1121.65086
Van De Vyver, Hans
An explicit Numerov-type method for second-order differential equations with oscillating solutions. (English)
[J] Comput. Math. Appl. 53, No. 9, 1339-1348 (2007). ISSN 0898-1221

Summary: A new explicit Numerov-type method is introduced. The construction is based on a modification of a sixth-order explicit Numerov-type method recently developed by {\it Ch. Tsitouras} [ibid. 45, 37--42 (2003; Zbl 1035.65078)]. Two free parameters are added in order to nullify the phase-lag and the amplification. The method is useful only when a good estimate of the frequency of the problem is known in advance. The parameters depend on the product of the estimated frequency and the stepsize. Numerical results obtained for well-known test problems show the efficiency of the new method.

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: second-order initial-value problems; Numerov-type methods; oscillating solutions; phase fitting; variable coefficients; numerical results

Citations: Zbl 1035.65078

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