Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani
Numerical root finding is the technique of approximating the roots of an equation through numerical methods. Numerical method is often chosen for solving nonlinear functions rather than analytical approach. The main purpose of this project is to compare the numerical methods chosen which are Newton’...
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my.uitm.ir.1061782024-11-30T22:55:59Z https://ir.uitm.edu.my/id/eprint/106178/ Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani Zailani, Iman Muneera Analytical methods used in the solution of physical problems Numerical root finding is the technique of approximating the roots of an equation through numerical methods. Numerical method is often chosen for solving nonlinear functions rather than analytical approach. The main purpose of this project is to compare the numerical methods chosen which are Newton’s method, Steffensen’s method, Shah and Noor’s First method, and Shah and Noor’s Second method to see which one is best for solving eight nonlinear functions, using Maple software, from four different types of functions which are trigonometric function, exponential function, quadratic function, and polynomial function using four different initial values with three stopping criteria. This is done by running programming code, based on the methods chosen, using Maple software. The comparison is based on the number of iterations, CPU time, and accuracy. The results via performance profile using SigmaPlot show that Newton’s method is overall the best method for all the criteria for its high level of efficiency and robustness. Both Shah and Noor’s First method and Shah and Noor’s Second method show comparable results with each other while Steffensen’s method shows the worst performance. 2024 Thesis NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/106178/1/106178.pdf Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani. (2024) Degree thesis, thesis, Universiti Teknologi MARA, Terengganu. |
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Analytical methods used in the solution of physical problems |
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Analytical methods used in the solution of physical problems Zailani, Iman Muneera Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani |
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Numerical root finding is the technique of approximating the roots of an equation through numerical methods. Numerical method is often chosen for solving nonlinear functions rather than analytical approach. The main purpose of this project is to compare the numerical methods chosen which are Newton’s method, Steffensen’s method, Shah and Noor’s First method, and Shah and Noor’s Second method to see which one is best for solving eight nonlinear functions, using Maple software, from four different types of functions which are trigonometric function, exponential function, quadratic function, and polynomial function using four different initial values with three stopping criteria. This is done by running programming code, based on the methods chosen, using Maple software. The comparison is based on the number of iterations, CPU time, and accuracy. The results via performance profile using SigmaPlot show that Newton’s method is overall the best method for all the criteria for its high level of efficiency and robustness. Both Shah and Noor’s First method and Shah and Noor’s Second method show comparable results with each other while Steffensen’s method shows the worst performance. |
| format |
Thesis |
| author |
Zailani, Iman Muneera |
| author_facet |
Zailani, Iman Muneera |
| author_sort |
Zailani, Iman Muneera |
| title |
Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani |
| title_short |
Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani |
| title_full |
Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani |
| title_fullStr |
Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani |
| title_full_unstemmed |
Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani |
| title_sort |
solving nonlinear equations using shah and noor’s iterative method / iman muneera zailani |
| publishDate |
2024 |
| url |
https://ir.uitm.edu.my/id/eprint/106178/1/106178.pdf https://ir.uitm.edu.my/id/eprint/106178/ |
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1817847344899555328 |
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13.222552 |