A generalized form of an approximate solution to a strongly non-linear, second-order, differential equation

Abstract

An approximate solution, in terms of Jacobian elliptic functions, of the equation $ with $ was developed in Christopher (1973). A generalization of this method, applicable to the class of equations $ with $, is developed. When applied to the case where $ the method is not subject to the restriction c ₁ − b ²/4 > 0. A numerical comparison for this latter case shows that the now technique is still accurate over a wide range of values of b and c ₃. Some falling off of accuracy is experienced when b/c ₃ > 0·5.