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He, J.H. (2003) A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International Journal of Non-Linear Mechanics, 35, 37-43. doi:10.1016/S0020-7462(98)00085-7

has been cited by the following article:

• TITLE: Analytical solution of coupled non-linear second order differential equations in enzyme kinetics

  AUTHORS: Govindhan Varadharajan, Lakshmanan Rajendran

  KEYWORDS: Non-Linear Reaction Equations; Mathematical Modelling; Steady-State; Homotopy Perturbation Method; Simulation

  JOURNAL NAME: Natural Science, Vol.3 No.6, June 22, 2011

  ABSTRACT: The coupled system of non-linear second-order reaction differential equation in basic enzyme reaction is formulated and closed analytical ex-pressions for substrate and product concentra-tions are presented. Approximate analytical me-thod (He’s Homotopy perturbation method) is used to solve the coupled non-linear differential equations containing a non-linear term related to enzymatic reaction. Closed analytical expres-sions for substrate concentration, enzyme sub-strate concentration and product concentration have been derived in terms of dimensionless reaction diffusion parameters k, and us-ing perturbation method. These results are compared with simulation results and are found to be in good agreement. The obtained results are valid for the whole solution domain.