Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions

This thesis investigates on the numerical solutions for solving two-point and multipoint boundary value problems (BVPs) subject to Robin and mixed boundary conditions. The BVPs are solved directly using the new developed two-point diagonally implicit multistep block method in the form of Adams ty...

Full description

Saved in:

Bibliographic Details
Main Author:	Mohd Nasir, Nadirah
Format:	Thesis
Language:	English
Published:	2020
Subjects:	Boundary value problems Numerical analysis
Online Access:	http://psasir.upm.edu.my/id/eprint/104714/1/NADIRAH%20BINTI%20MOHD%20NASIR%20-%20IR.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-upm-ir.104714
record_format	uketd_dc
spelling	my-upm-ir.1047142023-10-05T04:35:05Z Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions 2020-07 Mohd Nasir, Nadirah This thesis investigates on the numerical solutions for solving two-point and multipoint boundary value problems (BVPs) subject to Robin and mixed boundary conditions. The BVPs are solved directly using the new developed two-point diagonally implicit multistep block method in the form of Adams type formula. Constant and variable step size strategy are employed for solving two-point second-order BVPs. Meanwhile, the computed solutions for two-point and multipoint third-order BVPs are limit to constant step size. Shooting technique is implemented in order to solve the BVPs. The initial estimate values are obtained using the Newton’s divided difference interpolation method and Steffensen’s method. Alternatively, the first derivative function is absence during the calculation of guessing values compared to the shooting technique via the Newton’s method. The analysis included order, error constants, consistency, zero-stability and convergence are presented in describing the characteristics of the proposed methods. All the computational procedures were undertaken using the C language in a Code::Blocks 16.01 cross platform. Numerical results showed significant findings where the proposed methods could offer better accuracy results, less costly in terms of total function calls and faster in timing compared to the existing methods. In conclusion, the proposed methods and developed algorithms were shown to be a reliable BVPs solver for solving two-point and multipoint BVPs subject to Robin and mixed boundary conditions directly. Boundary value problems Numerical analysis 2020-07 Thesis http://psasir.upm.edu.my/id/eprint/104714/ http://psasir.upm.edu.my/id/eprint/104714/1/NADIRAH%20BINTI%20MOHD%20NASIR%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Boundary value problems Numerical analysis Abdul Majid, Zanariah
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Abdul Majid, Zanariah
topic	Boundary value problems Numerical analysis
spellingShingle	Boundary value problems Numerical analysis Mohd Nasir, Nadirah Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions
description	This thesis investigates on the numerical solutions for solving two-point and multipoint boundary value problems (BVPs) subject to Robin and mixed boundary conditions. The BVPs are solved directly using the new developed two-point diagonally implicit multistep block method in the form of Adams type formula. Constant and variable step size strategy are employed for solving two-point second-order BVPs. Meanwhile, the computed solutions for two-point and multipoint third-order BVPs are limit to constant step size. Shooting technique is implemented in order to solve the BVPs. The initial estimate values are obtained using the Newton’s divided difference interpolation method and Steffensen’s method. Alternatively, the first derivative function is absence during the calculation of guessing values compared to the shooting technique via the Newton’s method. The analysis included order, error constants, consistency, zero-stability and convergence are presented in describing the characteristics of the proposed methods. All the computational procedures were undertaken using the C language in a Code::Blocks 16.01 cross platform. Numerical results showed significant findings where the proposed methods could offer better accuracy results, less costly in terms of total function calls and faster in timing compared to the existing methods. In conclusion, the proposed methods and developed algorithms were shown to be a reliable BVPs solver for solving two-point and multipoint BVPs subject to Robin and mixed boundary conditions directly.
format	Thesis
qualification_level	Doctorate
author	Mohd Nasir, Nadirah
author_facet	Mohd Nasir, Nadirah
author_sort	Mohd Nasir, Nadirah
title	Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions
title_short	Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions
title_full	Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions
title_fullStr	Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions
title_full_unstemmed	Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions
title_sort	multistep block method for solving second and third order boundary value problems with robin and mixed type boundary conditions
granting_institution	Universiti Putra Malaysia
publishDate	2020
url	http://psasir.upm.edu.my/id/eprint/104714/1/NADIRAH%20BINTI%20MOHD%20NASIR%20-%20IR.pdf
_version_	1783725835004411904

Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions

Similar Items