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Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy

A differential equation can be solved analytically or numerically. In many complicated cases, it is enough to just approximate the solution if the differential equation cannot be solved analytically. Euler's method, the improved Euler's method and Runge-Kutta methods are ex­amples of commo...

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Main Authors: Khata, Mohamad Nazri Mohamad, Radzali, Nur Habibah, Hilmy, Mohamad Aliff Afifuddin
Format: Student Project
Language:English
Published: 2017
Subjects:
Study and teaching
Equations
Data processing
Analysis
Online Access:https://ir.uitm.edu.my/id/eprint/109965/1/109965.pdf
https://ir.uitm.edu.my/id/eprint/109965/
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record_format eprints
spelling my.uitm.ir.1099652025-02-11T00:54:09Z https://ir.uitm.edu.my/id/eprint/109965/ Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy Khata, Mohamad Nazri Mohamad Radzali, Nur Habibah Hilmy, Mohamad Aliff Afifuddin Study and teaching Equations Data processing Analysis A differential equation can be solved analytically or numerically. In many complicated cases, it is enough to just approximate the solution if the differential equation cannot be solved analytically. Euler's method, the improved Euler's method and Runge-Kutta methods are ex­amples of commonly used numerical techniques in approximately solved differential equations. These methods are also called as single-step methods or starting methods because they use the value from one starting step to approximate the solution of the next step. While, multistep or continuing methods such as Adam-Bashforth and Adam-Moulton methods use the values from several computed steps to approximate the value of the next step. So, in terms of minimizing the calculating time in solving differential , multistep method is recommended by previous researchers. In this project, a Riccati differential equation is solved using the two multistep meth­ods in order to analyze the accuracy of both methods. Both methods give small errors when they are compared to the exact solution but it is identified that Adam-Bashforth method is more accurate than Adam-Moulton method. 2017 Student Project NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/109965/1/109965.pdf Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy. (2017) [Student Project] <http://terminalib.uitm.edu.my/109965.pdf> (Unpublished)
institution Universiti Teknologi Mara
building Tun Abdul Razak Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Mara
content_source UiTM Institutional Repository
url_provider http://ir.uitm.edu.my/
language English
topic Study and teaching
Equations
Data processing
Analysis
spellingShingle Study and teaching
Equations
Data processing
Analysis
Khata, Mohamad Nazri Mohamad
Radzali, Nur Habibah
Hilmy, Mohamad Aliff Afifuddin
Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy
description A differential equation can be solved analytically or numerically. In many complicated cases, it is enough to just approximate the solution if the differential equation cannot be solved analytically. Euler's method, the improved Euler's method and Runge-Kutta methods are ex­amples of commonly used numerical techniques in approximately solved differential equations. These methods are also called as single-step methods or starting methods because they use the value from one starting step to approximate the solution of the next step. While, multistep or continuing methods such as Adam-Bashforth and Adam-Moulton methods use the values from several computed steps to approximate the value of the next step. So, in terms of minimizing the calculating time in solving differential , multistep method is recommended by previous researchers. In this project, a Riccati differential equation is solved using the two multistep meth­ods in order to analyze the accuracy of both methods. Both methods give small errors when they are compared to the exact solution but it is identified that Adam-Bashforth method is more accurate than Adam-Moulton method.
format Student Project
author Khata, Mohamad Nazri Mohamad
Radzali, Nur Habibah
Hilmy, Mohamad Aliff Afifuddin
author_facet Khata, Mohamad Nazri Mohamad
Radzali, Nur Habibah
Hilmy, Mohamad Aliff Afifuddin
author_sort Khata, Mohamad Nazri Mohamad
title Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy
title_short Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy
title_full Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy
title_fullStr Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy
title_full_unstemmed Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy
title_sort technical report: numerical solutions of riccati equations using adam-bashforth and adam-moulton methods / mohamad nazri mohamad khata, nur habibah radzali and mohamad aliff afifuddin hilmy
publishDate 2017
url https://ir.uitm.edu.my/id/eprint/109965/1/109965.pdf
https://ir.uitm.edu.my/id/eprint/109965/
_version_ 1825165138476400640
score 13.239859

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