Numerical solution to solve Initial Value Problems (IVPs) of first-order ordinary differential equation using single-step and multistep methods / Nurul Nisrina Norwan

The numerical solution can be used to estimate the solution to several forms of ordinary differential equations (ODEs) through repeated iterations. Numerical solutions are also extremely crucial in scientific computation since they are broadly utilized to depict actual or real-world issues. Conseque...

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التفاصيل البيبلوغرافية
المؤلف الرئيسي:	Norwan, Nurul Nisrina
التنسيق:	أطروحة
اللغة:	English
منشور في:	2023
الموضوعات:	Difference equations Functional equations Delay differential equations Integral equations
الوصول للمادة أونلاين:	https://ir.uitm.edu.my/id/eprint/97772/1/97772.pdf
الوسوم:	إضافة وسم لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!

id	my-uitm-ir.97772
record_format	uketd_dc
spelling	my-uitm-ir.977722024-07-27T17:56:32Z Numerical solution to solve Initial Value Problems (IVPs) of first-order ordinary differential equation using single-step and multistep methods / Nurul Nisrina Norwan 2023 Norwan, Nurul Nisrina Difference equations. Functional equations. Delay differential equations. Integral equations The numerical solution can be used to estimate the solution to several forms of ordinary differential equations (ODEs) through repeated iterations. Numerical solutions are also extremely crucial in scientific computation since they are broadly utilized to depict actual or real-world issues. Consequently, it is sufficient to determine the numerical approximation, which allows us to implement the various techniques to solve the differential equation numerically. The aim of applying the numerical solution is the desire to have the exact solution as possible. Moreover, the numerical solution with a high level of precision is commonly used to obtain the exact solution for the problem. Therefore, this project implements the single-step methods and the multistep methods for solving initial value problems of first-order ordinary differential equations. For the single-step method, the methods are EM, MEM, and RK4. Meanwhile, AB2, AB3, and AB4 explicit methods are used for the multistep method. Thereby in this project, the single-step RK4 has the highest level of accuracy for approximating the solutions of every IVPs. In the meantime, for each method used, the approximated solution approaches to the exact solution as the step size decreases. The smaller step size, h=0.0125 resulted in more preciseness for approximated solutions. Lastly, for the multistep method, a better approximation is obtained at a higher step of Adams-Bashforth, which is AB4. 2023 Thesis https://ir.uitm.edu.my/id/eprint/97772/ https://ir.uitm.edu.my/id/eprint/97772/1/97772.pdf text en public degree Universiti Teknologi MARA, Terengganu College of Computing, Informatics and Mathematics Salahudin, Nur Atikah
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Salahudin, Nur Atikah
topic	Difference equations Functional equations Delay differential equations Integral equations
spellingShingle	Difference equations Functional equations Delay differential equations Integral equations Norwan, Nurul Nisrina Numerical solution to solve Initial Value Problems (IVPs) of first-order ordinary differential equation using single-step and multistep methods / Nurul Nisrina Norwan
description	The numerical solution can be used to estimate the solution to several forms of ordinary differential equations (ODEs) through repeated iterations. Numerical solutions are also extremely crucial in scientific computation since they are broadly utilized to depict actual or real-world issues. Consequently, it is sufficient to determine the numerical approximation, which allows us to implement the various techniques to solve the differential equation numerically. The aim of applying the numerical solution is the desire to have the exact solution as possible. Moreover, the numerical solution with a high level of precision is commonly used to obtain the exact solution for the problem. Therefore, this project implements the single-step methods and the multistep methods for solving initial value problems of first-order ordinary differential equations. For the single-step method, the methods are EM, MEM, and RK4. Meanwhile, AB2, AB3, and AB4 explicit methods are used for the multistep method. Thereby in this project, the single-step RK4 has the highest level of accuracy for approximating the solutions of every IVPs. In the meantime, for each method used, the approximated solution approaches to the exact solution as the step size decreases. The smaller step size, h=0.0125 resulted in more preciseness for approximated solutions. Lastly, for the multistep method, a better approximation is obtained at a higher step of Adams-Bashforth, which is AB4.
format	Thesis
qualification_level	Bachelor degree
author	Norwan, Nurul Nisrina
author_facet	Norwan, Nurul Nisrina
author_sort	Norwan, Nurul Nisrina
title	Numerical solution to solve Initial Value Problems (IVPs) of first-order ordinary differential equation using single-step and multistep methods / Nurul Nisrina Norwan
title_short	Numerical solution to solve Initial Value Problems (IVPs) of first-order ordinary differential equation using single-step and multistep methods / Nurul Nisrina Norwan
title_full	Numerical solution to solve Initial Value Problems (IVPs) of first-order ordinary differential equation using single-step and multistep methods / Nurul Nisrina Norwan
title_fullStr	Numerical solution to solve Initial Value Problems (IVPs) of first-order ordinary differential equation using single-step and multistep methods / Nurul Nisrina Norwan
title_full_unstemmed	Numerical solution to solve Initial Value Problems (IVPs) of first-order ordinary differential equation using single-step and multistep methods / Nurul Nisrina Norwan
title_sort	numerical solution to solve initial value problems (ivps) of first-order ordinary differential equation using single-step and multistep methods / nurul nisrina norwan
granting_institution	Universiti Teknologi MARA, Terengganu
granting_department	College of Computing, Informatics and Mathematics
publishDate	2023
url	https://ir.uitm.edu.my/id/eprint/97772/1/97772.pdf
_version_	1811768876824788992

Numerical solution to solve Initial Value Problems (IVPs) of first-order ordinary differential equation using single-step and multistep methods / Nurul Nisrina Norwan

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