Numerical calculation of the frequency of an oscillatory problem
In recent times, a number of special numerical methods has been proposed for the integration of oscillatory problems of the form \(x''+\omega^2x=\varepsilon f(x,x')\). These methods depend on the frequency of the oscillation. A rough approximation is given by \(\omega\). The authors show how it can easily be improved using the first approximation of Krylov and Bogolyubov. In three numerical experiments with a code developed by the authors, it is shown that the numerical results become much better, if the improved approximation for the frequency is used. The examples include the Duffing oscillator, two coupled anharmonic oscillators and a satellite problem in focal variables.
scientific article; zbMATH DE number 1428511