A hybrid functions approach for the Duffing equation

In this paper, a new numerical method for solving the Duffing equation is presented. We consider this equation in two forms, with integral boundary conditions and involving both integral and non-integral forcing terms. The method is based on a hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrix of integration is given. This matrix is then utilized to reduce the solution of the Duffing equation to a nonlinear equation. Illustrative examples are included to demonstrate the validity and applicability of the technique. (paper)