Approximation of solutions for an initial and terminal value problem for the forced Duffing equation with non-viscous damping

An algorithm to find explicit approximate solutions of an initial and terminal value problem for the forced Duffing equation with non-viscous damping is accomplished via a generalized quasilinearization method. In fact, we obtain a monotone sequence of approximate solutions converging uniformly and quadratically to a unique solution of the problem.