Approximation of solutions of the nonlinear Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions

In this paper, we study a boundary value problem involving the nonlinear Duffing equation with both integral and non-integral forcing terms, and separated boundary conditions. We develop a generalized quasilinearization algorithm to obtain monotone sequences of lower and upper solutions converging uniformly and quadratically to the unique solution of the problem.