Improved numerical integration of perturbed oscillators via average
Devoting special attention to oscillatory problems, the present paper addresses the improvement of numerical integration results provided by general purpose codes and by special algorithms. This technique based on the Kryloff-Bogoliuboff method allows us to perform some preconditioning work on the differential equations governing the dynamics of the problem in order to obtain better results when we use a general purpose code, such as Runge-Kutta or Adams methods. The authors reduce the error growth in the long-term integration with special numerical methods by using the improved frequency provided by the first approximation of \textit{N. Kryloff} and \textit{N. Bogoliuboff} [Introduction to nonlinear mechanics, Princeton Univ. Press, Princeton, NJ (1947; MR 4.142)]. Numerical examples are given.
scientific article; zbMATH DE number 1311109
scientific article