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:
Online Access:http://psasir.upm.edu.my/id/eprint/70475/1/FS%202014%2049%20IR.pdf
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author Mohd Zawawi, Iskandar Shah
author_facet Mohd Zawawi, Iskandar Shah
author_sort Mohd Zawawi, Iskandar Shah
collection UPM
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.
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spelling upm.eprints-704752019-10-30T03:26:27Z http://psasir.upm.edu.my/id/eprint/70475/ Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations 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. 2014-01 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/70475/1/FS%202014%2049%20IR.pdf Mohd Zawawi, Iskandar Shah (2014) Diagonally implicit two point block backward differentiation formulas for solving stiff ordinary differential equations and fuzzy differential equations. Masters thesis, Universiti Putra Malaysia. 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
title 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_short 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
topic Stiff computation (Differential equations)
Differential equations - Numerical solutions
url http://psasir.upm.edu.my/id/eprint/70475/1/FS%202014%2049%20IR.pdf
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