Analysis of non-linear reaction-diffusion processes with Michaelis-Menten kinetics by a new Homotopy perturbation method

Devaraj  Shanthi; Vembu  Ananthaswamy; Lakshmanan  Rajendran

doi:10.4236/ns.2013.59128

Devaraj Shanthi, Vembu Ananthaswamy, Lakshmanan Rajendran

Abstract: This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.

Keywords: Oxygen Diffusion; Michaelis-Menten; Non-Linear Differential Equations; New Homotopy Perturbation Method; Numerical Simulation

Cite this paper: Shanthi, D. , Ananthaswamy, V. and Rajendran, L. (2013) Analysis of non-linear reaction-diffusion processes with Michaelis-Menten kinetics by a new Homotopy perturbation method. Natural Science, 5, 1034-1046. doi: 10.4236/ns.2013.59128.

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