Extended Parker–Sochacki method for Michaelis–Menten enzymatic reaction model

•Parker-Sochacki method is utilized to obtain power series solutions for Michaelis-Menten enzymatic model.•The method is extended through the use of a new resummation method to acquire approximate analytical solutions.•The proposed method does not require a small parameter or an initial solution and it gives a global form for the solution.•Comparing the results with numerical results proves the applicability and the accuracy of the proposed method.•The proposed method serves as a basis for solving other nonlinear biochemical reaction models.

In this article, a new approach—namely, the extended Parker–Sochacki method (EPSM)—is presented for solving the Michaelis–Menten nonlinear enzymatic reaction model. The Parker–Sochacki method (PSM) is combined with a new resummation method called the Sumudu–Padé resummation method to obtain approximate analytical solutions for the model. The obtained solutions by the proposed approach are compared with the solutions of PSM and the Runge–Kutta numerical method (RKM). The comparison proves the practicality, efficiency, and correctness of the presented approach. It serves as a basis for solving other nonlinear biochemical reaction models in the future.

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