In this paper, a constructed Green's function coupled with a fixed point iteration scheme will be employed to solve nonlinear dynamical problems that arise in electroanalytical chemistry. More precisely, the method will be used to mathematically model and solve the kinetics of the amperometric enzyme. A main property that makes the proposed method superior to other iterative methods is the way it handles boundary value problems, where both endpoints are taken into consideration while other iterative methods only make account of the initial point and as a result, the approximate solution may deteriorate for values that are far away from the initial point and closer to the other endpoint. Through tests on some known amperometric enzyme kinetics, the proposed method gave more accurate results than many numerical schemes that were employed for this purpose. The method is found to be easily implemented, fast, and computationally economical and attractive. (C) 2017 Elsevier B.V. All rights reserved.