Generalization of the Störmer method for perturbed oscillators without explicit first derivatives
This paper is concerned with the numerical treatment of perturbed oscillators. A new family of multistep methods is developed that avoid the calculation of the first derivative. The new methods generalize the Störmer and Cowell codes and have the same leading error terms as the Bettis codes [cf. \textit{D. G. Bettis}, Numer. Math. 14, 421-434 (1970; Zbl 0198.49601)]. Numerical experiments and comparisons show the good behaviour of the presented methods.
scientific article; zbMATH DE number 1398823
scientific article