Extension and improvement to the Krylov–Bogoliubov methods using elliptic functions
S. B. Yuste, J.D. Bejarano · International Journal of Control · 1989
It is shown that the Krylov–Bogoliubov methods that give the approximate oscillatory solution of the equation in terms of Jacobi elliptic functions are applicable not only when c 1>0 and c 3>0, but also when c 1>0 and c 30. In particular, the most precise of these methods, the Christopher-Brocklehurst method, is discussed in detail. Its accuracy has been improved by utilizing the transformation properties of elliptic functions with respect to their parameters.