Phase-lag analysis of explicit Nyström methods for \(y''=f(x,y)\) (Q1079344)

A two-parameter family of explicit Nyström methods of fourth order proposed by the first author and \textit{S. Sharma} [ibid. 21, 455-464 (1981; Zbl 0469.65048)] are discussed in the case of the equation \(y''+a^ 2y=0\). It turns out that two of them are optimal with regard to the so called ''phase lag'', introduced in the above mentioned paper. The results are illustrated by numerical examples.