Approximate analytic methods for the solution of a class of strongly non-linear differential equations--a comparison

Abstract

A review is made of certain approximate analytic methods which are capable of solving a wide class of strongly nonlinear, ordinary, differential equations. Contained in this class are many equations which arise from the analysis of physical situations, e.g. the equation of Van der Pol and the unforced Duffing equation. The relative accuracy of these methods is assessed by applying them to a particular strongly nonlinear equation and comparing the solutions with numerical solutions obtained on a digital computer. The results show the R.A.E. and CJ. methods to be a useful and accurate means of solving this particular equation over a wide range of the coefficients involved.