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An efficient wavelet based approximation method to steady state reaction-diffusion model arising in mathematical

M Mahalakshmi1, G Hariharan

  • 1Department of Mathematics, School of Humanities & Sciences, SASTRA University, Thanjavur, 613401, Tamilnadu, India.

The Journal of Membrane Biology
|January 22, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a novel wavelet method for solving complex biosensor models. The shifted second kind Chebyshev wavelets (CW) offer an efficient and accurate approach for reaction-diffusion equations in amperometric biosensors.

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Area of Science:

  • Applied Mathematics
  • Biochemical Engineering
  • Computational Chemistry

Background:

  • Amperometric biosensors rely on mathematical models to describe enzyme kinetics and diffusion.
  • Reaction-diffusion equations with nonlinear terms, such as Michaelis-Menton kinetics, are crucial for modeling these biosensors.
  • Existing models may require more efficient numerical solutions.

Purpose of the Study:

  • To apply the shifted second kind Chebyshev wavelets (CW) for numerical solutions of reaction-diffusion equations in amperometric biosensor models.
  • To evaluate the efficiency, accuracy, and applicability of the CW method for these specific problems.
  • To validate the mathematical model proposed by Rahamathunissa and Rajendran (2008).

Main Methods:

  • The study employs the shifted second kind Chebyshev wavelets (CW) operational matrices.
  • This method is applied to solve initial and boundary value problems associated with reaction-diffusion equations.
  • The nonlinear term is based on Michaelis-Menton kinetics, representing enzymatic reactions.

Main Results:

  • The numerical results demonstrate the efficiency and applicability of the proposed shifted second kind CW method.
  • The method provides accurate solutions for the reaction-diffusion equations.
  • The computational cost is found to be small, making the method attractive.

Conclusions:

  • The shifted second kind Chebyshev wavelets (CW) method is a powerful, simple, and accurate technique for solving amperometric biosensor models.
  • The method is computationally attractive and efficient for reaction-diffusion equations with Michaelis-Menton kinetics.
  • The findings confirm the manageability and effectiveness of the CW approach in this context.