Analyzing accuracy: a comparative study of Trapezoidal rules, Simpson’s rules, Weddle’s rules, and Midpoint rules / Nur Azza Shyafiqah Rosli

The moment it is impossible to determine a closed form of the integral or when an approximate value only of the definite integral is required, researchers can utilize numerical integration to estimate its values. The Midpoint rule, Trapezoidal rule, Simpson's rule, and Weddle’s rule are the met...

Full description

Saved in:

Bibliographic Details
Main Author:	Rosli, Nur Azza Shyafiqah
Format:	Thesis
Language:	English
Published:	2023
Subjects:	Analytical methods used in the solution of physical problems
Online Access:	https://ir.uitm.edu.my/id/eprint/97693/1/97693.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-uitm-ir.97693
record_format	uketd_dc
spelling	my-uitm-ir.976932024-07-27T16:57:39Z Analyzing accuracy: a comparative study of Trapezoidal rules, Simpson’s rules, Weddle’s rules, and Midpoint rules / Nur Azza Shyafiqah Rosli 2023 Rosli, Nur Azza Shyafiqah Analytical methods used in the solution of physical problems The moment it is impossible to determine a closed form of the integral or when an approximate value only of the definite integral is required, researchers can utilize numerical integration to estimate its values. The Midpoint rule, Trapezoidal rule, Simpson's rule, and Weddle’s rule are the methods for numerical integration that are most frequently utilized. The question of which of the five methods is the best yields a more precise response. By using the same subintervals, find the error of all methods. This project tries to investigate and analyze the behaviour of each numerical method. Calculate an approximate value for the area under the curve and calculate the error to determine which one chosen numerical integration methods is the best. The methods are: Trapezoidal rule, Simpson’s rule, Weddle rule, and Midpoint rule. As a result, it is possible to conclude that Weddle's Rule with a subinterval of n=96 is the most effective method based on the error. Simpson's 3/8 Rule is the best approach based on CPU Times; the best subinterval based on CPU Times is n=12 but the worst subinterval is n=96. It demonstrated that Weddle's Rule is the most effective numerical strategy for resolving challenging integration issues. It is advised to attempt more challenging integration issues based on various intervals and subintervals. Researchers could also introduce more numerical integration methods. 2023 Thesis https://ir.uitm.edu.my/id/eprint/97693/ https://ir.uitm.edu.my/id/eprint/97693/1/97693.pdf text en public degree Universiti Teknologi MARA, Terengganu College of Computing, Informatics and Mathematics Jaafar, Ruhana
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Jaafar, Ruhana
topic	Analytical methods used in the solution of physical problems
spellingShingle	Analytical methods used in the solution of physical problems Rosli, Nur Azza Shyafiqah Analyzing accuracy: a comparative study of Trapezoidal rules, Simpson’s rules, Weddle’s rules, and Midpoint rules / Nur Azza Shyafiqah Rosli
description	The moment it is impossible to determine a closed form of the integral or when an approximate value only of the definite integral is required, researchers can utilize numerical integration to estimate its values. The Midpoint rule, Trapezoidal rule, Simpson's rule, and Weddle’s rule are the methods for numerical integration that are most frequently utilized. The question of which of the five methods is the best yields a more precise response. By using the same subintervals, find the error of all methods. This project tries to investigate and analyze the behaviour of each numerical method. Calculate an approximate value for the area under the curve and calculate the error to determine which one chosen numerical integration methods is the best. The methods are: Trapezoidal rule, Simpson’s rule, Weddle rule, and Midpoint rule. As a result, it is possible to conclude that Weddle's Rule with a subinterval of n=96 is the most effective method based on the error. Simpson's 3/8 Rule is the best approach based on CPU Times; the best subinterval based on CPU Times is n=12 but the worst subinterval is n=96. It demonstrated that Weddle's Rule is the most effective numerical strategy for resolving challenging integration issues. It is advised to attempt more challenging integration issues based on various intervals and subintervals. Researchers could also introduce more numerical integration methods.
format	Thesis
qualification_level	Bachelor degree
author	Rosli, Nur Azza Shyafiqah
author_facet	Rosli, Nur Azza Shyafiqah
author_sort	Rosli, Nur Azza Shyafiqah
title	Analyzing accuracy: a comparative study of Trapezoidal rules, Simpson’s rules, Weddle’s rules, and Midpoint rules / Nur Azza Shyafiqah Rosli
title_short	Analyzing accuracy: a comparative study of Trapezoidal rules, Simpson’s rules, Weddle’s rules, and Midpoint rules / Nur Azza Shyafiqah Rosli
title_full	Analyzing accuracy: a comparative study of Trapezoidal rules, Simpson’s rules, Weddle’s rules, and Midpoint rules / Nur Azza Shyafiqah Rosli
title_fullStr	Analyzing accuracy: a comparative study of Trapezoidal rules, Simpson’s rules, Weddle’s rules, and Midpoint rules / Nur Azza Shyafiqah Rosli
title_full_unstemmed	Analyzing accuracy: a comparative study of Trapezoidal rules, Simpson’s rules, Weddle’s rules, and Midpoint rules / Nur Azza Shyafiqah Rosli
title_sort	analyzing accuracy: a comparative study of trapezoidal rules, simpson’s rules, weddle’s rules, and midpoint rules / nur azza shyafiqah rosli
granting_institution	Universiti Teknologi MARA, Terengganu
granting_department	College of Computing, Informatics and Mathematics
publishDate	2023
url	https://ir.uitm.edu.my/id/eprint/97693/1/97693.pdf
_version_	1811768873541697536

Analyzing accuracy: a comparative study of Trapezoidal rules, Simpson’s rules, Weddle’s rules, and Midpoint rules / Nur Azza Shyafiqah Rosli

Similar Items