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S. J. Liao, “Beyond Perturbation: Introduction to the Homotopy Analysis Method,” Chapman and Hall, CRC Press, Boca Raton, 2003, p. 336.

has been cited by the following article:

• TITLE: Analytical Expressions of Concentrations inside the Cationic Glucose-Sensitive Membrane

  AUTHORS: Swaminathan Sevukaperumal, Shunmugham Loghambal, Lakshmanan Rajendran

  KEYWORDS: Homotopy Analysis Method; Cationic Glucose-Sensitive Membrane; Non-Linear Reaction/Diffusion Equations

  JOURNAL NAME: Applied Mathematics, Vol.3 No.4, April 27, 2012

  ABSTRACT: A mathematical model of Wu et al. [J. Membr. Sci 254 (2005) 119-127] of a cationic glucose-sensitive membrane is discussed. The model involves the system of non-linear steady-state reaction-diffusion equations. Analytical expres-sions pertaining to concentration of oxygen, glucose, and gluconic acid for all values of parameters are presented. We have employed Homotopy analysis method to evaluate the approximate analytical solutions of the non-linear boundary value problem. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed.