An explicit hybrid method of Numerov type for second-order periodic initial-value problems (Q1899970)

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 \[ y''(t)= Ay(t)+ g(t, y(t)),\quad t_0\leq t< \infty.\tag{i} \] The algorithm is fourth-order four stage of Numerov type, and is designed to have minimal frequency distortion when \(g\equiv 0\) [cf. \textit{M. M. Chawla} and \textit{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.