Solution of bacteria- surface decontamination model by using separation of variables
The aim of this study is to investigate the application of the Fourier series method to solve a known mathematical model of surface disinfection and in order to determine its effectiveness. The mathematical model is based on the reaction-diffusion partial differential equation due to the diffusion o...
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my-utm-ep.1019352023-07-25T09:34:59Z Solution of bacteria- surface decontamination model by using separation of variables 2019 Al Farsi, Khalifa Ali Abdallah QA Mathematics The aim of this study is to investigate the application of the Fourier series method to solve a known mathematical model of surface disinfection and in order to determine its effectiveness. The mathematical model is based on the reaction-diffusion partial differential equation due to the diffusion of the bacteria into the disinfectant solution when the decontamination process begins and the reaction of the disinfectant killing effect on the bacteria. Analytical and approximate solution for the model is carried out using Fourier series. The infinite Fourier series is approximated twice by choosing finite terms of the series and by approximating some of the eigenvalues of the solution. Mathematica programming software is selected to execute the numerical computations. The obtained results are compared with the exact initial condition and a previous study. Simulation of the results demonstrate that the Fourier series method is able to approximate the solution of the surface disinfection model. 2019 Thesis http://eprints.utm.my/id/eprint/101935/ http://eprints.utm.my/id/eprint/101935/1/KhalifaAliAbdallahMFS2019.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146262 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science |
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Universiti Teknologi Malaysia |
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UTM Institutional Repository |
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English |
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QA Mathematics |
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QA Mathematics Al Farsi, Khalifa Ali Abdallah Solution of bacteria- surface decontamination model by using separation of variables |
| description |
The aim of this study is to investigate the application of the Fourier series method to solve a known mathematical model of surface disinfection and in order to determine its effectiveness. The mathematical model is based on the reaction-diffusion partial differential equation due to the diffusion of the bacteria into the disinfectant solution when the decontamination process begins and the reaction of the disinfectant killing effect on the bacteria. Analytical and approximate solution for the model is carried out using Fourier series. The infinite Fourier series is approximated twice by choosing finite terms of the series and by approximating some of the eigenvalues of the solution. Mathematica programming software is selected to execute the numerical computations. The obtained results are compared with the exact initial condition and a previous study. Simulation of the results demonstrate that the Fourier series method is able to approximate the solution of the surface disinfection model. |
| format |
Thesis |
| qualification_level |
Master's degree |
| author |
Al Farsi, Khalifa Ali Abdallah |
| author_facet |
Al Farsi, Khalifa Ali Abdallah |
| author_sort |
Al Farsi, Khalifa Ali Abdallah |
| title |
Solution of bacteria- surface decontamination model by using separation of variables |
| title_short |
Solution of bacteria- surface decontamination model by using separation of variables |
| title_full |
Solution of bacteria- surface decontamination model by using separation of variables |
| title_fullStr |
Solution of bacteria- surface decontamination model by using separation of variables |
| title_full_unstemmed |
Solution of bacteria- surface decontamination model by using separation of variables |
| title_sort |
solution of bacteria- surface decontamination model by using separation of variables |
| granting_institution |
Universiti Teknologi Malaysia, Faculty of Science |
| granting_department |
Faculty of Science |
| publishDate |
2019 |
| url |
http://eprints.utm.my/id/eprint/101935/1/KhalifaAliAbdallahMFS2019.pdf |
| _version_ |
1776100807055245312 |