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**Wavelet method for steady state immobilized enzyme kinetic model: an operational matrix approach.**
*(English)*
Zbl 1471.92138

Summary: This paper discusses a mathematical model of the diffusion and reaction in amperometric biosensor response with immobilized enzyme electrodes within a uniform film. This model contains a nonlinear differential equation related to Michaelis-Menten kinetics. In this paper, shifted Legendre wavelet method (SLWM) has been applied to obtain the mediator and substrate concentrations. The efficiency of the method is confirmed by means of the computational run time. The obtained approximate solutions are compared with the available results. Satisfactory agreement with homotopy perturbation method (HPM) and relaxation method (RM) is observed. Moreover, the shifted Legendre wavelet method is found to be simple, efficient and computationally attractive.

### MSC:

92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |

92C47 | Biosensors (not for medical applications) |

### Keywords:

amperometric enzyme electrodes; Michaelis-Menten kinetics; shifted Legendre wavelet method; homotopy perturbation method (HPM)
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\textit{G. Hariharan} and \textit{S. Padma}, J. Math. Chem. 59, No. 9, 1994--2008 (2021; Zbl 1471.92138)

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### References:

[1] | Bartlett, PN; Pratt, KFE, Theoretical treatment of diffusion and kinetics in amperometric immobilized enzyme electrodes Part I: Redox mediator entrapped within the film, J. Electroanal. Chem., 397, 61-78 (1995) |

[2] | Loghambal, S.; Rajendran, L., Mathematical modeling of diffusion and kinetics in amperometric immobilized enzyme electrodes, Electrochimica Acta, 55, 5230-5238 (2010) |

[3] | Hariharan. G. Haar, Wavelet Method for Solving the Klein-Gordon and the Sine-Gordon Equations, International Journal of Nonlinear Science, 11, 2, 180-189 (2011) · Zbl 1235.35246 |

[4] | Rajaraman, R.; Hariharan, G., An efficient wavelet based spectral methods to singular boundary value problems, Journal of Mathematical Chemistry, 53, 9, 2095-2113 (2015) · Zbl 1329.65333 |

[5] | ] Mahalakshmi.M., Hariharan.G., ‘An efficient wavelet based approximation method to steady state reaction-diffusion model arising in mathematical chemistry’, Journal of Mathematical Chemistry, 2015, doi 10, 1007/s 10910-015-0560-0. · Zbl 1351.92061 |

[6] | Padma S., Hariharan G., Wavelet Based Analytical Expressions to Steady State Biofilm Model Arising in Biochemical Engineering’, Journal of Membrane Biology, Doi doi:10.1007/s00232-015-9861-2 |

[7] | Hariharan, G., An efficient legendre wavelet-based approximation methodfor a few newell-whitehead and allen-cahn equations, J. Membr. Biol., 247, 5, 371-380 (2014) |

[8] | Mohammadi, F.; Hosseini, MM, A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations, J Franklin Institute, 348, 1787-1796 (2011) · Zbl 1237.65079 |

[9] | Mohammadi, F.; Hosseini, MM, Legendre wavelet method for solving linear stiff systems, J Adv Res Differential equ, 2, 1, 47-57 (2010) |

[10] | Fukang Yin, Junqiang Song ,Solving Linear PDEs with the Aid of Two-Dimensional Legendre Wavelets, National Conference on Information Technology and Computer Science (CITCS 2012) |

[11] | Razzaghi, M.; Yousefi, S., Legendre Wavelets Method for the solution of Nonlinear problems in the calculus of variations, Math. Comput. Model., 34, 45-54 (2001) · Zbl 0991.65053 |

[12] | Mohammadi, F., An extended Legendre wavelet method for solving differential equation with non-analytic solution, Journal of Mathematical Extension, 8, 4, 55-74 (2014) · Zbl 1355.65103 |

[13] | Vazquez-Leal, H.; Boubaker, K., ‘Quadratic Riccati differential equation in particle physics, Nonlinear Sci. Lett. A, 8, 1, 1-10 (2017) |

[14] | Cakir, M.; Arslan, D., The adomian decomposition method and the differential transform method for numerical solution of multi-pantograph delay differential equations, Appl. Math., 6, 1332-1343 (2015) |

[15] | Taghavi, A.; Babaei, A.; Mohammadpour, A., ’Analytical approximations of the porous medium equations by reduced differential transform method’, Int J Adv Appl Math Mech, 2, 3, 95-100 (2015) · Zbl 1359.35105 |

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