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An explicit hybrid method of Numerov type for second-order periodic initial-value problems. (English) Zbl 0844.65061

The author introduces and tests a new algorithm for approximation to periodic solutions of a nonlinearly perturbed system of linear ordinary differential equations having the form

y '' (t)=Ay(t)+g(t,y(t)),t 0 t<·(i)

The algorithm is fourth-order four stage of Numerov type, and is designed to have minimal frequency distortion when g0 [cf. M. M. Chawla and P. S. Rao, J. Comput. Appl. Math. 15, 329-337 (1986; Zbl 0598.65054)].

Numerical results obtained with four test problems indicate that the new method performs better than other methods of Numerov type as well as methods using symplectic integrations and the LSODE code.

65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34C25Periodic solutions of ODE
34A34Nonlinear ODE and systems, general