Abstract
In this chapter, wavelet-based operational matrix methods have been developed to investigate the approximate solutions for amperometric enzyme kinetic problems. The operational matrices of derivatives have been utilized for solving the nonlinear initial value problems. The accuracy of the proposed wavelet-based approximation methods has been confirmed. The main purpose of the proposed method is to get better and more accurate results. Operational matrices of Chebyshev and Legendre wavelets are utilized to obtain a sequence of discrete equations into the systems of algebraic equations and the solutions of algebraic systems lead to the solution of nonlinear initial value problems. Numerical experiments are given to demonstrate the accuracy and efficiency of the proposed method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
K. Indira, L. Rajendran, Analytical expression of the concentration and substrates and product in phenol-polyphenol oxidase system immobilised in laponite hydrogels. Michelis–Menten formalism in homogeneous medium. Electrochim. Acta 56, 6411–6419 (2011)
P.N. Bartlett, R.G. Whitaker, Electrochemical immobilization of enzyme: part-I theory. J. Electroanal. Chem. Interfacial Electrochem. 224, 27–35 (1987)
R. Baronas, F. Ivanauskas, J. Kulys, M. Sapagovas, Modeling of amperometric biosensors with rough surface of the enzyme membrane. J. Math. Chem. 34, 227–242 (2003)
R. Baronas, J. Kulys, F. Ivanauskas, Modelling amperometric enzyme electrode with substrate cyclic conversion. Biosens. Bioelectron. 19, 915–922 (2004)
L. Rajendran, S. Anitha, Reply to “Comments on Analytical solution of amperometric enzymatic reactions based on HPM” by J.-H. He, L.-F. Mo. Electrochim. Acta 102, 474–476 (2013)
J.-H. He, X.-H. Wu, Variational iteration method-new development and applications. Comput. Math. Appl. 54, 881–894 (2007)
A. Malvandi, D.D. Ganji, A general mathematical expression of amperometric enzyme kinetics using He’s variational iteration method with Pade approximation. J. Electroanal. Chem. 711, 32–37 (2013)
J.-H. He, L.-F. Mo, Comments on “Analytical solution of amperometric enzymatic reactions based on HPM” by A. Shanmugarajan, S. Alwarappan, S. Somasundaram, R. Lakshmanan. Electrochim. Acta 102, 472–473 (2013)
H. He, Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng. 178, 257–262 (1999)
G. Rahamathunissa, L. Rajendran, Application of He’s variational iteration method in nonlinear boundary value problems in enzyme substrate reaction diffusion processes. J. Math. Chem. 44, 849–861 (2008)
A. Meena, L. Rajendran, Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations—homotopy perturbation technique. J. Electroanal. Chem. 644, 50–59 (2010)
A. Eswari, L. Rajendran, Analytical expressions of concentration and current in homogeneous catalytic reactions at spherical microelectrodes: homotopy perturbation approach. J. Electroanal. Chem. 651, 173–184 (2011)
A. Shanmugarajan, S. Alwarappan, S. Somasundaram, R. Lakshmanan, Analytical solution of amperometric enzymatic reactions based on homotopy perturbation method. Electrochim. Acta 56, 3345–3352 (2011)
E.H. Doha, A.H. Bhrawy, S.S. Ezz Eldien, Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations. Appl. Math. Modell. 35, 5662–5672 (2011)
D. Sathyaseelan, G. Hariharan, Wavelet-Based Approximation Algorithms for Some Nonlinear Oscillator Equations Arising in Engineering. J. Inst. Eng. India Ser. C (Article in press)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Hariharan, G. (2019). Analytical Expressions of Amperometric Enzyme Kinetics Pertaining to the Substrate Concentration Using Wavelets. In: Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-32-9960-3_6
Download citation
DOI: https://doi.org/10.1007/978-981-32-9960-3_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-32-9959-7
Online ISBN: 978-981-32-9960-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)