An application of Least Square method and Steepest Descent method for solving second order differential equation / Nurun Najwa Mohd Faizail
Ordinary differential equations (ODE) are one of the important and widely used techniques in mathematical modelling. This method requires finding the solution theoretically. However, some of the theoretical method uses to find the solutions are extremely complicated. Least Square method is one of th...
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my-uitm-ir.399762020-12-31T02:07:38Z An application of Least Square method and Steepest Descent method for solving second order differential equation / Nurun Najwa Mohd Faizail 2018-07 Mohd Faizail, Nurun Najwa Mathematical statistics. Probabilities Data processing Analytical methods used in the solution of physical problems Ordinary differential equations (ODE) are one of the important and widely used techniques in mathematical modelling. This method requires finding the solution theoretically. However, some of the theoretical method uses to find the solutions are extremely complicated. Least Square method is one of the numerical methods that can be used for finding an approximation for the solution of ODE without solving it theoretically. However, this method requires finding the inverse of matrix which sometime does not exist for a singular matrix. Thus, to avoid this problem Steepest Descent method is used together with Least Square method. This research analyses the efficiency of least square method and Steepest Descent method for the approximation of ODE solution numerically compared to the theoretical solution. Result shows that the numerical solution approximation is comparable to the theoretical solution without finding the true solution. 2018-07 Thesis https://ir.uitm.edu.my/id/eprint/39976/ https://ir.uitm.edu.my/id/eprint/39976/1/39976.pdf text en public degree Universiti Teknologi MARA Faculty of Computer and Mathematical Sciences Mohd Ali, Mohd Rivaie |
| institution |
Universiti Teknologi MARA |
| collection |
UiTM Institutional Repository |
| language |
English |
| advisor |
Mohd Ali, Mohd Rivaie |
| topic |
Mathematical statistics Probabilities Data processing Analytical methods used in the solution of physical problems |
| spellingShingle |
Mathematical statistics Probabilities Data processing Analytical methods used in the solution of physical problems Mohd Faizail, Nurun Najwa An application of Least Square method and Steepest Descent method for solving second order differential equation / Nurun Najwa Mohd Faizail |
| description |
Ordinary differential equations (ODE) are one of the important and widely used techniques in mathematical modelling. This method requires finding the solution theoretically. However, some of the theoretical method uses to find the solutions are extremely complicated. Least Square method is one of the numerical methods that can be used for finding an approximation for the solution of ODE without solving it theoretically. However, this method requires finding the inverse of matrix which sometime does not exist for a singular matrix. Thus, to avoid this problem Steepest Descent method is used together with Least Square method. This research analyses the efficiency of least square method and Steepest Descent method for the approximation of ODE solution numerically compared to the theoretical solution. Result shows that the numerical solution approximation is comparable to the theoretical solution without finding the true solution. |
| format |
Thesis |
| qualification_level |
Bachelor degree |
| author |
Mohd Faizail, Nurun Najwa |
| author_facet |
Mohd Faizail, Nurun Najwa |
| author_sort |
Mohd Faizail, Nurun Najwa |
| title |
An application of Least Square method and Steepest Descent method for solving second order differential equation / Nurun Najwa Mohd Faizail |
| title_short |
An application of Least Square method and Steepest Descent method for solving second order differential equation / Nurun Najwa Mohd Faizail |
| title_full |
An application of Least Square method and Steepest Descent method for solving second order differential equation / Nurun Najwa Mohd Faizail |
| title_fullStr |
An application of Least Square method and Steepest Descent method for solving second order differential equation / Nurun Najwa Mohd Faizail |
| title_full_unstemmed |
An application of Least Square method and Steepest Descent method for solving second order differential equation / Nurun Najwa Mohd Faizail |
| title_sort |
application of least square method and steepest descent method for solving second order differential equation / nurun najwa mohd faizail |
| granting_institution |
Universiti Teknologi MARA |
| granting_department |
Faculty of Computer and Mathematical Sciences |
| publishDate |
2018 |
| url |
https://ir.uitm.edu.my/id/eprint/39976/1/39976.pdf |
| _version_ |
1783734548828258304 |