Journal of Computational and Applied Mathematics
An explicit sixth-order method with phase-lag of order eight for y″=f(t,y)
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
High-order P-stable multistep methods
Journal of Computational and Applied Mathematics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Mixed collocation methods for y′′=fx,y
Journal of Computational and Applied Mathematics
A phase-fitted collocation-based Runge-Kutta-Nyström method
Applied Numerical Mathematics
An optimized Runge-Kutta method for the solution of orbital problems
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
A class of explicit two-step hybrid methods for second-order IVPs
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Frequency evaluation for exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics
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In this paper 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 Tsitouras [Ch. Tsitouras, Explicit Numerov type methods with reduced number of stages, Comput. Math. Appl. 45 (2003) 37-42]. 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.