A semi-analytical solution of amperometric enzymatic reactions based on Green's functions and fixed point iterative schemes

Abstract In this paper, a constructed Green's function coupled with a fixed point iteration scheme will be employed to solve nonlinear dynamical problems that arise in electroanalytical chemistry. More precisely, the method will be used to mathematically model and solve the kinetics of the amperometric enzyme. A main property that makes the proposed method superior to other iterative methods is the way it handles boundary value problems, where both endpoints are taken into consideration while other iterative methods only make account of the initial point and as a result, the approximate solution may deteriorate for values that are far away from the initial point and closer to the other endpoint. Through tests on some known amperometric enzyme kinetics, the proposed method gave more accurate results than many numerical schemes that were employed for this purpose. The method is found to be easily implemented, fast, and computationally economical and attractive.

[1]  Suheil A. Khuri,et al.  A novel fixed point iteration method for the solution of third order boundary value problems , 2015, Appl. Math. Comput..

[2]  A. A. Soliman,et al.  New applications of variational iteration method , 2005 .

[3]  Feliksas Ivanauskas,et al.  An Analysis of Mixtures Using Amperometric Biosensors and Artificial Neural Networks , 2004 .

[4]  Hui Xu,et al.  Potential diagnostic applications of biosensors: current and future directions , 2006, International journal of nanomedicine.

[5]  Ji-Huan He,et al.  Variational iteration method: New development and applications , 2007, Comput. Math. Appl..

[6]  Lakshmanan Rajendran,et al.  Application of He’s variational iteration method in nonlinear boundary value problems in enzyme– substrate reaction diffusion processes: part 1. The steady-state amperometric response , 2008 .

[7]  Ji-Huan He.  Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[8]  Asha Chaubey,et al.  Application of conducting polymers to biosensors. , 2002, Biosensors & bioelectronics.

[9]  Subbiah Alwarappan,et al.  Analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method , 2011 .

[10]  G. S. Wilson,et al.  Biosensors : fundamentals and applications , 1987 .

[11]  A. Malvandi,et al.  A general mathematical expression of amperometric enzyme kinetics using He’s variational iteration method with Padé approximation , 2013 .

[12]  C. Pao.  Mathematical analysis of enzyme-substrate reaction diffusion in some biochemical systems , 1980 .

[13]  F. Ivanauskas,et al.  Modelling of Amperometric Biosensors with Rough Surface of the Enzyme Membrane , 2003 .

[14]  Suheil A. Khuri,et al.  A novel fixed point scheme: Proper setting of variational iteration method for BVPs , 2015, Appl. Math. Lett..

[15]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[16]  Lakshmanan Rajendran,et al.  System of coupled non-linear reaction diffusion processes at conducting polymer-modified ultramicroelectrodes , 2010 .

[17]  M. Abukhaled.  Variational Iteration Method for Nonlinear Singular Two-Point Boundary Value Problems Arising in Human Physiology , 2013 .

[18]  M. Mahalakshmi,et al.  An efficient Chebyshev wavelet based analytical algorithm to steady state reaction–diffusion models arising in mathematical chemistry , 2015, Journal of Mathematical Chemistry.