Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations

Our main contribution in the thesis is the development of a new block method which is called diagonally implicit two point block backward differentiation formulas of order two (DI2BBDF(2)), order three (DI2BBDF(3)) and order four (DI2BBDF(4)) for solving stiff ordinary differential equations (ODEs)...

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Main Author:	Mohd Zawawi, Iskandar Shah
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Stiff computation (Differential equations) Differential equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/70475/1/FS%202014%2049%20IR.pdf
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id	my-upm-ir.70475
record_format	uketd_dc
spelling	my-upm-ir.704752019-10-30T03:26:27Z Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations 2014-01 Mohd Zawawi, Iskandar Shah Our main contribution in the thesis is the development of a new block method which is called diagonally implicit two point block backward differentiation formulas of order two (DI2BBDF(2)), order three (DI2BBDF(3)) and order four (DI2BBDF(4)) for solving stiff ordinary differential equations (ODEs) and fuzzy differential equations (FDEs). This method is constructed to compute multiple approximations concurrently in a block using various back values. The performance of the method is compared with existing methods. Furthermore, the convergence and stability properties of the method are investigated. The strategy of choosing suitable step size is also discussed. This thesis also explored the numerical solution of first order FDEs. The fully implicit two point block backward differentiation formulas of order three (FI2BBDF(3)) is reviewed and modified in fuzzy version for solving fuzzy initial value problems (FIVPs) under a new interpretation of Hukuhara Differentiability Theorem (HDT). Based on HDT, the exact and approximated solutions for two cases are compared to investigate the accuracy of the method. Finally, the derived method is modified in fuzzy version for solving FIVPs under HDT. The efficiency of the method is compared with several existing methods. In conclusion, the proposed method can be an alternative method for solving stiff ODEs and FDEs. Stiff computation (Differential equations) Differential equations - Numerical solutions 2014-01 Thesis http://psasir.upm.edu.my/id/eprint/70475/ http://psasir.upm.edu.my/id/eprint/70475/1/FS%202014%2049%20IR.pdf text en public masters Universiti Putra Malaysia Stiff computation (Differential equations) Differential equations - Numerical solutions
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Stiff computation (Differential equations) Differential equations - Numerical solutions
spellingShingle	Stiff computation (Differential equations) Differential equations - Numerical solutions Mohd Zawawi, Iskandar Shah Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations
description	Our main contribution in the thesis is the development of a new block method which is called diagonally implicit two point block backward differentiation formulas of order two (DI2BBDF(2)), order three (DI2BBDF(3)) and order four (DI2BBDF(4)) for solving stiff ordinary differential equations (ODEs) and fuzzy differential equations (FDEs). This method is constructed to compute multiple approximations concurrently in a block using various back values. The performance of the method is compared with existing methods. Furthermore, the convergence and stability properties of the method are investigated. The strategy of choosing suitable step size is also discussed. This thesis also explored the numerical solution of first order FDEs. The fully implicit two point block backward differentiation formulas of order three (FI2BBDF(3)) is reviewed and modified in fuzzy version for solving fuzzy initial value problems (FIVPs) under a new interpretation of Hukuhara Differentiability Theorem (HDT). Based on HDT, the exact and approximated solutions for two cases are compared to investigate the accuracy of the method. Finally, the derived method is modified in fuzzy version for solving FIVPs under HDT. The efficiency of the method is compared with several existing methods. In conclusion, the proposed method can be an alternative method for solving stiff ODEs and FDEs.
format	Thesis
qualification_level	Master's degree
author	Mohd Zawawi, Iskandar Shah
author_facet	Mohd Zawawi, Iskandar Shah
author_sort	Mohd Zawawi, Iskandar Shah
title	Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations
title_short	Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations
title_full	Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations
title_fullStr	Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations
title_full_unstemmed	Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations
title_sort	diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2014
url	http://psasir.upm.edu.my/id/eprint/70475/1/FS%202014%2049%20IR.pdf
_version_	1747812846692990976

Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations

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