Multiblock Backward Differentiation Formulae for solving first order ordinary differential equations

Block Backward Differentiation Formulae (BBDF) methods of variable order is derived to solve first order stiff ordinary differential equations (ODEs). These methods computed two approximate solutions yn+1 and yn+2 at the points xn+1 and xn+2 of the initial value problems (lVPs) concurrently in a...

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Main Author:	Mohd Nasir, Nor Ain Azeany
Format:	Thesis
Language:	English
Published:	2011
Subjects:	Differential equations - Numerical solutions Numerical analysis
Online Access:	http://psasir.upm.edu.my/id/eprint/84987/1/FS%202011%2066%20ir.pdf
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id	my-upm-ir.84987
record_format	uketd_dc
spelling	my-upm-ir.849872021-12-31T02:57:37Z Multiblock Backward Differentiation Formulae for solving first order ordinary differential equations 2011-11 Mohd Nasir, Nor Ain Azeany Block Backward Differentiation Formulae (BBDF) methods of variable order is derived to solve first order stiff ordinary differential equations (ODEs). These methods computed two approximate solutions yn+1 and yn+2 at the points xn+1 and xn+2 of the initial value problems (lVPs) concurrently in a block at each step. The numerical results are given to validate the method and the performancers are being compared with the classical Backward Differentiation Formulae (BBDF) methods Furthermore, the stability properties and the stability regions for the BBDF methods are investigated to ensure the methods are useful for solving stiff ODEs. This BBDF is extended to variable order method in order to improve the efficiency of the method. A single code is developed with fixed stepsize and implemented using Microsoft Visual C++ 2008 Express Edition and compared with ode 15s and ode 23s which is run in MATLAB 7.1. A parallel scheme of the BBDF is derived in order to solve large problems in ODEs using the Message Passing Interface (MPI) library run by the High Performance Computer (HPC). The efficiency of the method is justified by the numerical results given. The results generated showed that these methods produced less computional time and achieved the desired accuracy. Differential equations - Numerical solutions Numerical analysis 2011-11 Thesis http://psasir.upm.edu.my/id/eprint/84987/ http://psasir.upm.edu.my/id/eprint/84987/1/FS%202011%2066%20ir.pdf text en public masters Universiti Putra Malaysia Differential equations - Numerical solutions Numerical analysis Ibrahim, Zarina Bibi
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Ibrahim, Zarina Bibi
topic	Differential equations - Numerical solutions Numerical analysis
spellingShingle	Differential equations - Numerical solutions Numerical analysis Mohd Nasir, Nor Ain Azeany Multiblock Backward Differentiation Formulae for solving first order ordinary differential equations
description	Block Backward Differentiation Formulae (BBDF) methods of variable order is derived to solve first order stiff ordinary differential equations (ODEs). These methods computed two approximate solutions yn+1 and yn+2 at the points xn+1 and xn+2 of the initial value problems (lVPs) concurrently in a block at each step. The numerical results are given to validate the method and the performancers are being compared with the classical Backward Differentiation Formulae (BBDF) methods Furthermore, the stability properties and the stability regions for the BBDF methods are investigated to ensure the methods are useful for solving stiff ODEs. This BBDF is extended to variable order method in order to improve the efficiency of the method. A single code is developed with fixed stepsize and implemented using Microsoft Visual C++ 2008 Express Edition and compared with ode 15s and ode 23s which is run in MATLAB 7.1. A parallel scheme of the BBDF is derived in order to solve large problems in ODEs using the Message Passing Interface (MPI) library run by the High Performance Computer (HPC). The efficiency of the method is justified by the numerical results given. The results generated showed that these methods produced less computional time and achieved the desired accuracy.
format	Thesis
qualification_level	Master's degree
author	Mohd Nasir, Nor Ain Azeany
author_facet	Mohd Nasir, Nor Ain Azeany
author_sort	Mohd Nasir, Nor Ain Azeany
title	Multiblock Backward Differentiation Formulae for solving first order ordinary differential equations
title_short	Multiblock Backward Differentiation Formulae for solving first order ordinary differential equations
title_full	Multiblock Backward Differentiation Formulae for solving first order ordinary differential equations
title_fullStr	Multiblock Backward Differentiation Formulae for solving first order ordinary differential equations
title_full_unstemmed	Multiblock Backward Differentiation Formulae for solving first order ordinary differential equations
title_sort	multiblock backward differentiation formulae for solving first order ordinary differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/84987/1/FS%202011%2066%20ir.pdf
_version_	1747813508848812032

Multiblock Backward Differentiation Formulae for solving first order ordinary differential equations

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