Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions

A sequence of approximate solutions converging monotonically and quadratically to the unique solution of the forced Duffing equation with integral boundary conditions is obtained. We also establish the convergence of order k(k⩾2) for the sequence of iterates. The results obtained in this paper offer an algorithm to study the various practical phenomena such as prediction of the possible onset of vascular diseases, onset of chaos in speech, etc. Some interesting observations are presented.