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Liao, S.J. and Tan, Y. (2007) A general approach to obtain series solutions of nonlinear differential equations. Studies in Applied Mathematics, 119, 297-355. doi:10.1111/j.1467-9590.2007.00387.x

has been cited by the following article:

• TITLE: Analytical expressions of steady-state concentrations of species in potentiometric and amperometric biosensor

  AUTHORS: Mayakkannan Sivasankari, Lakshmanan Rajendran

  KEYWORDS: Enzyme Electrodes; Enzyme Reactors; Potentiometry; Amperometry; Homotopy Analysis Method; Biosensor

  JOURNAL NAME: Natural Science, Vol.4 No.12, December 19, 2012

  ABSTRACT: A mathematical model of potentiometric and amperometric enzyme electrodes is discussed. The model is based on the system of non-linear steady-state coupled reaction diffusion equations for Michaelis-Menten formalism that describe the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate, product and corresponding flux response have been derived for all values of parameters using Homotopy analysis method. The obtained solution allow a full characterization of the response curves for only two kinetic parameters (The Michaelis constant and the ratio of overall reaction and the diffusion rates). A simple relation between the concentration of substrate and products for all values of parameter is also reported. All the analytical results are compared with simulation results (Scilab/Matlab program). The simulated results are agreed with the appropriate theories. The obtained theoretical results are valid for the whole solution domain.