Diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations

In this study, two-point diagonally implicit multistep block methods are proposed for solving single first order ordinary and fuzzy differential equations. The methods are based on the diagonally implicit multistep block methods. It approximates two points simultaneously at n 1 y  and n 2 y  in a...

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Main Author:	Ramli, Azizah
Format:	Thesis
Language:	English
Published:	2015
Subjects:	Mathematics General subdivision Research Differential equations Fuzzy mathematics
Online Access:	http://psasir.upm.edu.my/id/eprint/58926/1/IPM%202015%2013IR.pdf
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id	my-upm-ir.58926
record_format	uketd_dc
spelling	my-upm-ir.589262018-02-14T06:36:02Z Diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations 2015-12 Ramli, Azizah In this study, two-point diagonally implicit multistep block methods are proposed for solving single first order ordinary and fuzzy differential equations. The methods are based on the diagonally implicit multistep block methods. It approximates two points simultaneously at n 1 y  and n 2 y  in a block along the interval. Subsequently, the methods of order three, four and five are implemented and numerically tested using constant step size. The numerical results show that the two-point diagonally implicit multistep block methods could solve the ordinary differential equations without any difficulty. These methods are also able to reduce the number of steps and execution times even when the number of iterations is being increased. Meanwhile, the first order fuzzy differential equations is interpreted based on Seikkala’s derivative. By including characterization theorem, the fuzzy differential equations can be replaced by the equivalent system of ordinary differential equations. The numerical results show that the two-point diagonally implicit multistep block methods could solve the fuzzy differential equations. The accuracy of the approximate solutions is obtained by means of implementation of the method under the Seikkala’s derivative interpretation. Nevertheless, these methods respectively have the advantage in terms of reducing the number of function evaluations, total steps and execution times. In conclusion, the diagonally implicit multistep block methods are suitable for solving the single first order ordinary and fuzzy differential equations. Mathematics General subdivision Research Differential equations Fuzzy mathematics 2015-12 Thesis http://psasir.upm.edu.my/id/eprint/58926/ http://psasir.upm.edu.my/id/eprint/58926/1/IPM%202015%2013IR.pdf application/pdf en public masters Universiti Putra Malaysia Mathematics General subdivision Research Differential equations Fuzzy mathematics
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Mathematics General subdivision Research Differential equations Fuzzy mathematics
spellingShingle	Mathematics General subdivision Research Differential equations Fuzzy mathematics Ramli, Azizah Diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations
description	In this study, two-point diagonally implicit multistep block methods are proposed for solving single first order ordinary and fuzzy differential equations. The methods are based on the diagonally implicit multistep block methods. It approximates two points simultaneously at n 1 y  and n 2 y  in a block along the interval. Subsequently, the methods of order three, four and five are implemented and numerically tested using constant step size. The numerical results show that the two-point diagonally implicit multistep block methods could solve the ordinary differential equations without any difficulty. These methods are also able to reduce the number of steps and execution times even when the number of iterations is being increased. Meanwhile, the first order fuzzy differential equations is interpreted based on Seikkala’s derivative. By including characterization theorem, the fuzzy differential equations can be replaced by the equivalent system of ordinary differential equations. The numerical results show that the two-point diagonally implicit multistep block methods could solve the fuzzy differential equations. The accuracy of the approximate solutions is obtained by means of implementation of the method under the Seikkala’s derivative interpretation. Nevertheless, these methods respectively have the advantage in terms of reducing the number of function evaluations, total steps and execution times. In conclusion, the diagonally implicit multistep block methods are suitable for solving the single first order ordinary and fuzzy differential equations.
format	Thesis
qualification_level	Master's degree
author	Ramli, Azizah
author_facet	Ramli, Azizah
author_sort	Ramli, Azizah
title	Diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations
title_short	Diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations
title_full	Diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations
title_fullStr	Diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations
title_full_unstemmed	Diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations
title_sort	diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations
granting_institution	Universiti Putra Malaysia
publishDate	2015
url	http://psasir.upm.edu.my/id/eprint/58926/1/IPM%202015%2013IR.pdf
_version_	1747812226552561664

Diagonally implicit multistep block methods for solving first order ordinary and fuzzy equations

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