Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations

Block Backward Differentiation Formulae (BBDF) method with variable step variable order approach (VSVO) for solving stiff Ordinary Differential Equations (ODEs) is described in this thesis. The research on Variable Step Variable Order Block Backward Differentiation Formulae (VSVO-BBDF) method is div...

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Main Author:	Mohd Yatim, Siti Ainor
Format:	Thesis
Language:	English
Published:	2013
Subjects:	Differential equations
Online Access:	http://psasir.upm.edu.my/id/eprint/38845/1/FS%202013%2029%20IR.pdf
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spelling	my-upm-ir.388452016-04-06T04:02:07Z Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations 2013-07 Mohd Yatim, Siti Ainor Block Backward Differentiation Formulae (BBDF) method with variable step variable order approach (VSVO) for solving stiff Ordinary Differential Equations (ODEs) is described in this thesis. The research on Variable Step Variable Order Block Backward Differentiation Formulae (VSVO-BBDF) method is divided into two parts where the first part attempts to solve first order stiff ODEs, whereby second order stiff ODEs are considered subsequently. Initially, the computation of Dth-order variable step BBDF (VS-BBDF) method of order three up to five is presented. The detailed algorithms of VSVO-BBDF method is discussed to show the crucial parts of the order and stepsize selections. Prior to getting the numerical results, the MATLAB’s suite of ODEs solvers namely ode15s and ode23s is applied for the numerical comparison purposes. Meanwhile, the consistency and zero stability properties that lead to the convergence of the method are also discussed. Finally, the implementation of the VSVO-BBDF(2) method for the solution of second order stiff ODEs is analyzed. The derivation of the method of order two up to four, as well as the strategies in choosing the order and stepsize are elaborated. Similarly, numerical results are obtained after a fair comparison is made between VSVO-BBDF(2) and stiff ODEs solvers in MATLAB. In conclusion, the results display positive trends in reducing the total number of steps and increasing the accuracy of the approximations. The results also show that VSVO-BBDF method reduces the time execution for solving first and second order stiff ODEs as compared to MATLAB’s ODEs solvers. Therefore, these methods serve the purpose of significant alternatives for solving stiff ODEs. Differential equations 2013-07 Thesis http://psasir.upm.edu.my/id/eprint/38845/ http://psasir.upm.edu.my/id/eprint/38845/1/FS%202013%2029%20IR.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Differential equations
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Differential equations
spellingShingle	Differential equations Mohd Yatim, Siti Ainor Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations
description	Block Backward Differentiation Formulae (BBDF) method with variable step variable order approach (VSVO) for solving stiff Ordinary Differential Equations (ODEs) is described in this thesis. The research on Variable Step Variable Order Block Backward Differentiation Formulae (VSVO-BBDF) method is divided into two parts where the first part attempts to solve first order stiff ODEs, whereby second order stiff ODEs are considered subsequently. Initially, the computation of Dth-order variable step BBDF (VS-BBDF) method of order three up to five is presented. The detailed algorithms of VSVO-BBDF method is discussed to show the crucial parts of the order and stepsize selections. Prior to getting the numerical results, the MATLAB’s suite of ODEs solvers namely ode15s and ode23s is applied for the numerical comparison purposes. Meanwhile, the consistency and zero stability properties that lead to the convergence of the method are also discussed. Finally, the implementation of the VSVO-BBDF(2) method for the solution of second order stiff ODEs is analyzed. The derivation of the method of order two up to four, as well as the strategies in choosing the order and stepsize are elaborated. Similarly, numerical results are obtained after a fair comparison is made between VSVO-BBDF(2) and stiff ODEs solvers in MATLAB. In conclusion, the results display positive trends in reducing the total number of steps and increasing the accuracy of the approximations. The results also show that VSVO-BBDF method reduces the time execution for solving first and second order stiff ODEs as compared to MATLAB’s ODEs solvers. Therefore, these methods serve the purpose of significant alternatives for solving stiff ODEs.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mohd Yatim, Siti Ainor
author_facet	Mohd Yatim, Siti Ainor
author_sort	Mohd Yatim, Siti Ainor
title	Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations
title_short	Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations
title_full	Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations
title_fullStr	Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations
title_full_unstemmed	Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations
title_sort	variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2013
url	http://psasir.upm.edu.my/id/eprint/38845/1/FS%202013%2029%20IR.pdf
_version_	1747811757903052800

Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations

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