Some Numerical Methods and Comparisons for Solving Mathematical Model of Surface Decontamination by Disinfectant Solution

Authors

  • Chai Jin Sian Department of Mathematical Sciences, Faculty of Science, UTM
  • Yeak Su Hoe Department of Mathematical Sciences, Faculty of Science, UTM
  • Ali H. M. Murid Department of Mathematical Sciences, Faculty of Science, UTM

DOI:

https://doi.org/10.11113/matematika.v34.n2.1055

Abstract

A mathematical model is considered to determine the effectiveness of disinfectant solution for surface decontamination. The decontamination process involved the diffusion of bacteria into disinfectant solution and the reaction of the disinfectant killing effect. The mathematical model is a reaction-diffusion type. Finite difference method and method of lines with fourth-order Runge-Kutta method are utilized to solve the model numerically. To obtain stable solutions, von Neumann stability analysis is employed to evaluate the stability of finite difference method. For stiff problem, Dormand-Prince method is applied as the estimated error of fourth-order Runge-Kutta method. MATLAB programming is selected for the computation of numerical solutions. From the results obtained, fourth-order Runge-Kutta method has a larger stability region and better accuracy of solutions compared to finite difference method when solving the disinfectant solution model. Moreover, a numerical simulation is carried out to investigate the effect of different thickness of disinfectant solution on bacteria reduction. Results show that thick disinfectant solution is able to reduce the dimensionless bacteria concentration more effectively

Author Biographies

Chai Jin Sian, Department of Mathematical Sciences, Faculty of Science, UTM

Postgraduate student

department of Mathematical Science,

Faculty of Science,

Universiti Teknologi Malaysia

Yeak Su Hoe, Department of Mathematical Sciences, Faculty of Science, UTM

senior lecturer,

department of Mathematical Science,

Faculty of Science,

Universiti Teknologi Malaysia

Ali H. M. Murid, Department of Mathematical Sciences, Faculty of Science, UTM

Assoc. Prof.,

department of Mathematical Science,

Faculty of Science,

Universiti Teknologi Malaysia

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Published

2018-12-30

How to Cite

Jin Sian, C., Hoe, Y. S., & Murid, A. H. M. (2018). Some Numerical Methods and Comparisons for Solving Mathematical Model of Surface Decontamination by Disinfectant Solution. MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics, 34(2), 271–291. https://doi.org/10.11113/matematika.v34.n2.1055

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Section

Articles