A numerical scheme aimed at solving a broad class of second-order nonlinear boundary value problems (BVPs) is presented, described, and then applied to a problem that appears in chemical reactor theory. In particular, the steady-state solution of the equation governing the model of the adiabatic tubular chemical reactor is investigated. The proposed method is based on expressing the particular solution of the governing equation in terms of an integral involving Green's function. Then, the Krasnoselskii-Mann's fixed-point scheme is implemented to an amended version of the resulting integral operator. The convergence of the iterative scheme is proved and its efficiency and applicability are demonstrated by solving the equation for selected values of the parameters that appear in the model. Residual error computation is adopted to confirm the accuracy of the results. In addition, the numerical outcomes of the proposed method are compared with those obtained by other existing numerical approaches.