A comparison of HPM, NDHPM, Picard and Picard–Padé methods for solving Michaelis–Menten equation

The fact that physical phenomena are modelled, mostly, by nonlinear differential equations underlines the importance of having reliable methods to solve them. In this work, we present a comparison of homotopy perturbation method (HPM), nonlinearities distribution homotopy perturbation method (NDHPM), Picard, and Picard–Padé methods to solve Michaelis–Menten equation. The results show that NDHPM possesses the smallest average absolute relative error 1.51(−2) of all tested methods, in the range of r∈[0,5]r∈[0,5]. Also, we introduce the combination of Picard’s iterative method and Padé approximants as an alternative to reduce complexity of Picard’s solutions and increase accuracy.