An extension to the method of Kryloff and Bogoliuboff†

Abstract

An extension of the method of Kryloff and Bogoliuboff is presented which uses Jacobian elliptic functions to approximate the solutions to a class of second-order differential equations exhibiting a gross cubic non-linearity. The results obtained from an analysis of the error incurred by the approximation show that, provided certain conditions of smallness are satisfied, excellent solution accuracy can be obtained. Two examples are used to demonstrate application of the extension to systems of practical interest.