Application of least square method and conjugate gradient method for solving second order differential equation / Nur Fatonah Kamsani

Nowadays, solving second-order nonhomogeneous ordinary differential equations with Boundary Value Problem (BVP) is very important as it is commonly appeared in wide range of fields and professions such as physics and engineering. Usually, there are two theoretical methods used to solve this problem...

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Main Author:	Kamsani, Nur Fatonah
Format:	Thesis
Language:	English
Published:	2018
Subjects:	Mathematical statistics Probabilities Analysis Algorithms
Online Access:	https://ir.uitm.edu.my/id/eprint/40936/1/40936.pdf
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id	my-uitm-ir.40936
record_format	uketd_dc
spelling	my-uitm-ir.409362021-01-26T02:37:58Z Application of least square method and conjugate gradient method for solving second order differential equation / Nur Fatonah Kamsani 2018-07 Kamsani, Nur Fatonah Mathematical statistics. Probabilities Analysis Algorithms Nowadays, solving second-order nonhomogeneous ordinary differential equations with Boundary Value Problem (BVP) is very important as it is commonly appeared in wide range of fields and professions such as physics and engineering. Usually, there are two theoretical methods used to solve this problem which are undetermined coefficient and variation of parameters.. However, these theoretical methods are quite complicated, difficult to understand and take time. Researcher tends to use numerical method in the form of least square method which is quite simple and easy compared to the theoretical method. In this research, there are five ode problem selected and solved by using both theoretical and least square method. The functions selected are based on theoretical problem which are trigonometric, algebraic and exponential. Towards the end of least square method, Conjugate Gradient is used to solve the inverse matrix to avoid ill-conditioned matrix. The error is analysed based on solution of both exact and approximate methods. Numerical results show that Least Square Method can solve second-order nonhomogeneous ordinary differential equations with BVP in terms of the error analysis made by both theoretical and numerical methods. 2018-07 Thesis https://ir.uitm.edu.my/id/eprint/40936/ https://ir.uitm.edu.my/id/eprint/40936/1/40936.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 Analysis Algorithms
spellingShingle	Mathematical statistics Probabilities Analysis Algorithms Kamsani, Nur Fatonah Application of least square method and conjugate gradient method for solving second order differential equation / Nur Fatonah Kamsani
description	Nowadays, solving second-order nonhomogeneous ordinary differential equations with Boundary Value Problem (BVP) is very important as it is commonly appeared in wide range of fields and professions such as physics and engineering. Usually, there are two theoretical methods used to solve this problem which are undetermined coefficient and variation of parameters.. However, these theoretical methods are quite complicated, difficult to understand and take time. Researcher tends to use numerical method in the form of least square method which is quite simple and easy compared to the theoretical method. In this research, there are five ode problem selected and solved by using both theoretical and least square method. The functions selected are based on theoretical problem which are trigonometric, algebraic and exponential. Towards the end of least square method, Conjugate Gradient is used to solve the inverse matrix to avoid ill-conditioned matrix. The error is analysed based on solution of both exact and approximate methods. Numerical results show that Least Square Method can solve second-order nonhomogeneous ordinary differential equations with BVP in terms of the error analysis made by both theoretical and numerical methods.
format	Thesis
qualification_level	Bachelor degree
author	Kamsani, Nur Fatonah
author_facet	Kamsani, Nur Fatonah
author_sort	Kamsani, Nur Fatonah
title	Application of least square method and conjugate gradient method for solving second order differential equation / Nur Fatonah Kamsani
title_short	Application of least square method and conjugate gradient method for solving second order differential equation / Nur Fatonah Kamsani
title_full	Application of least square method and conjugate gradient method for solving second order differential equation / Nur Fatonah Kamsani
title_fullStr	Application of least square method and conjugate gradient method for solving second order differential equation / Nur Fatonah Kamsani
title_full_unstemmed	Application of least square method and conjugate gradient method for solving second order differential equation / Nur Fatonah Kamsani
title_sort	application of least square method and conjugate gradient method for solving second order differential equation / nur fatonah kamsani
granting_institution	Universiti Teknologi MARA
granting_department	Faculty of Computer and Mathematical Sciences
publishDate	2018
url	https://ir.uitm.edu.my/id/eprint/40936/1/40936.pdf
_version_	1783734604380766208

Application of least square method and conjugate gradient method for solving second order differential equation / Nur Fatonah Kamsani

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