Numerical verification and comparison of error of asymptotic expansion solution of the duffing equation

Abstract

A numerical order verification technique is applied to demonstrate that the asymptotic expansions of solutions of the Duffing equation obtained respectively by the Lindstedt-Poincaré(LP) method and the modified Lindstedt-Poincaré(MLP) method are uniformly valid for small parameter values. A numerical comparison of error shows that the MLP method is valid whereas the LP method is invalid for large parameter values.