Direct two-point block methods for solving nonstiff higher order Ordinary Differential Equations using Backward Difference formulation

This thesis describes the development of a Two-Point Block Backward Difference method (2PBBD) for solving system of nonstiff higher order Ordinary Differential Equations (ODEs) directly. The method computes the approximate solutions; and at two points and simultaneously within an equidistant block....

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Main Author:	Mohd Ijam, Hazizah
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Differential equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/52093/1/FS%202014%208RR.pdf
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id	my-upm-ir.52093
record_format	uketd_dc
spelling	my-upm-ir.520932017-05-03T03:12:02Z Direct two-point block methods for solving nonstiff higher order Ordinary Differential Equations using Backward Difference formulation 2014-09 Mohd Ijam, Hazizah This thesis describes the development of a Two-Point Block Backward Difference method (2PBBD) for solving system of nonstiff higher order Ordinary Differential Equations (ODEs) directly. The method computes the approximate solutions; and at two points and simultaneously within an equidistant block. This method has the advantages of calculating the integration coefficients only once at the beginning of the integration. The relationship between the explicit and implicit coefficients has also been derived. These motivate us to formulate the association between the formula for predictor and corrector. The relationship between the lower and higher order derivative also have been established. New explicit and implicit block methods using constant step sizes and three back values have also been derived. The algorithm developed is implemented using Microsoft Visual C++ 6.0 and run by High Performance Computer (HPC) using the Message Passing Interface (MPI) library. The stability properties for the 2PBBD methods are analyzed to ensure its suitability for solving nonstiff Initial Value Problems (IVPs). The stability analysis shows that the method is stable.Numerical results are presented to compare the performances of this method with the previously published One-Point Backward Difference (1PBD) and Two-Point Block Divided Difference (2PBDD) methods. The numerical results indicated that for finer step sizes, 2PBBD performs better than 1PBD and 2PBDD. Differential equations - Numerical solutions 2014-09 Thesis http://psasir.upm.edu.my/id/eprint/52093/ http://psasir.upm.edu.my/id/eprint/52093/1/FS%202014%208RR.pdf application/pdf en public masters Universiti Putra Malaysia Differential equations - Numerical solutions
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Differential equations - Numerical solutions
spellingShingle	Differential equations - Numerical solutions Mohd Ijam, Hazizah Direct two-point block methods for solving nonstiff higher order Ordinary Differential Equations using Backward Difference formulation
description	This thesis describes the development of a Two-Point Block Backward Difference method (2PBBD) for solving system of nonstiff higher order Ordinary Differential Equations (ODEs) directly. The method computes the approximate solutions; and at two points and simultaneously within an equidistant block. This method has the advantages of calculating the integration coefficients only once at the beginning of the integration. The relationship between the explicit and implicit coefficients has also been derived. These motivate us to formulate the association between the formula for predictor and corrector. The relationship between the lower and higher order derivative also have been established. New explicit and implicit block methods using constant step sizes and three back values have also been derived. The algorithm developed is implemented using Microsoft Visual C++ 6.0 and run by High Performance Computer (HPC) using the Message Passing Interface (MPI) library. The stability properties for the 2PBBD methods are analyzed to ensure its suitability for solving nonstiff Initial Value Problems (IVPs). The stability analysis shows that the method is stable.Numerical results are presented to compare the performances of this method with the previously published One-Point Backward Difference (1PBD) and Two-Point Block Divided Difference (2PBDD) methods. The numerical results indicated that for finer step sizes, 2PBBD performs better than 1PBD and 2PBDD.
format	Thesis
qualification_level	Master's degree
author	Mohd Ijam, Hazizah
author_facet	Mohd Ijam, Hazizah
author_sort	Mohd Ijam, Hazizah
title	Direct two-point block methods for solving nonstiff higher order Ordinary Differential Equations using Backward Difference formulation
title_short	Direct two-point block methods for solving nonstiff higher order Ordinary Differential Equations using Backward Difference formulation
title_full	Direct two-point block methods for solving nonstiff higher order Ordinary Differential Equations using Backward Difference formulation
title_fullStr	Direct two-point block methods for solving nonstiff higher order Ordinary Differential Equations using Backward Difference formulation
title_full_unstemmed	Direct two-point block methods for solving nonstiff higher order Ordinary Differential Equations using Backward Difference formulation
title_sort	direct two-point block methods for solving nonstiff higher order ordinary differential equations using backward difference formulation
granting_institution	Universiti Putra Malaysia
publishDate	2014
url	http://psasir.upm.edu.my/id/eprint/52093/1/FS%202014%208RR.pdf
_version_	1747812090723172352

Direct two-point block methods for solving nonstiff higher order Ordinary Differential Equations using Backward Difference formulation

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