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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 $$y''(t)= Ay(t)+ g(t, y(t)),\quad t_0\le t< \infty.\tag i$$ The algorithm is fourth-order four stage of Numerov type, and is designed to have minimal frequency distortion when $g\equiv 0$ [cf. {\it M. M. Chawla} and {\it 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
Full Text: DOI
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[2] Chawla, M. M.: Numerov made explicit has better stability. Bit 24, 117-118 (1984) · Zbl 0568.65042
[3] Chawla, M. M.; Rao, P. S.: A numerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. J. comput. Appl. math. 11, 277-281 (1984) · Zbl 0565.65041
[4] Chawla, M. M.; Rao, P. S.: A numerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: explicit method. J. comput. Appl. math. 15, 329-337 (1986) · Zbl 0598.65054
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[10] Meneguette, M.: Chawla-numerov method revisited. J. comput. Appl. math. 36, 247-250 (1991) · Zbl 0751.65048
[11] Sanz-Serna, J. M.: Symplectic integrators for Hamiltonian problems: an overview. Acta numerica 1, 243-286 (1992) · Zbl 0762.65043
[12] Van Der Houwen, P. J.; Sommeijer, B. P.: Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions. SIAM J. Numer. anal. 24, 595-617 (1987) · Zbl 0624.65058
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