BDF a BBDF pro řešení diferenciálních rovnic
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Date
Authors
Elusakin, Opeyemi Racheal
ORCID
Advisor
Referee
Mark
D
Journal Title
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Publisher
Vysoké učení technické v Brně. Fakulta strojního inženýrství
Abstract
his thesis explores the Backward Differentiation Formula (BDF) and Block Backward Differentiation Formula (BBDF) methods for solving stiff ordinary differential equations (ODEs). BDF methods are known for their stability, which makes them effective for stiff problems, while BBDF methods enhance this by solving multiple steps simultaneously, improving both efficiency and stability. The research delves into the derivation, implementation, and analysis of these methods, with a focus on their stability and convergence characteristics. We derive BDF and BBDF methods from fundamental principles, Stability analysis is conducted using techniques such as the root locus method and stability region characterization. Numerical experiments are conducted to validate the theoretical findings, comparing the performance of BDF and BBDF methods of several variants . The results demonstrate the better stability and efficiency of BBDF methods in solving ODEs, . This work offers a comprehensive study of BDF and BBDF methods, providing insights into their practical applications and potential for further development.
his thesis explores the Backward Differentiation Formula (BDF) and Block Backward Differentiation Formula (BBDF) methods for solving stiff ordinary differential equations (ODEs). BDF methods are known for their stability, which makes them effective for stiff problems, while BBDF methods enhance this by solving multiple steps simultaneously, improving both efficiency and stability. The research delves into the derivation, implementation, and analysis of these methods, with a focus on their stability and convergence characteristics. We derive BDF and BBDF methods from fundamental principles, Stability analysis is conducted using techniques such as the root locus method and stability region characterization. Numerical experiments are conducted to validate the theoretical findings, comparing the performance of BDF and BBDF methods of several variants . The results demonstrate the better stability and efficiency of BBDF methods in solving ODEs, . This work offers a comprehensive study of BDF and BBDF methods, providing insights into their practical applications and potential for further development.
his thesis explores the Backward Differentiation Formula (BDF) and Block Backward Differentiation Formula (BBDF) methods for solving stiff ordinary differential equations (ODEs). BDF methods are known for their stability, which makes them effective for stiff problems, while BBDF methods enhance this by solving multiple steps simultaneously, improving both efficiency and stability. The research delves into the derivation, implementation, and analysis of these methods, with a focus on their stability and convergence characteristics. We derive BDF and BBDF methods from fundamental principles, Stability analysis is conducted using techniques such as the root locus method and stability region characterization. Numerical experiments are conducted to validate the theoretical findings, comparing the performance of BDF and BBDF methods of several variants . The results demonstrate the better stability and efficiency of BBDF methods in solving ODEs, . This work offers a comprehensive study of BDF and BBDF methods, providing insights into their practical applications and potential for further development.
Description
Keywords
Stiff ordinary differential equations, implicit linear multistep methods, stability analysis, convergence, initial value problems, Lagrange interpolation polynomials, backward differentiation formula (BDF), block backward differentiation formula (BBDF), stability polynomial, order, Matlab, Stiff ordinary differential equations, implicit linear multistep methods, stability analysis, convergence, initial value problems, Lagrange interpolation polynomials, backward differentiation formula (BDF), block backward differentiation formula (BBDF), stability polynomial, order, Matlab
Citation
ELUSAKIN, O. BDF a BBDF pro řešení diferenciálních rovnic [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2024.
Document type
Document version
Date of access to the full text
Language of document
en
Study field
bez specializace
Comittee
doc. Ing. Luděk Nechvátal, Ph.D. (předseda)
prof. RNDr. Miloslav Druckmüller, CSc. (místopředseda)
prof. Mgr. Pavel Řehák, Ph.D. (člen)
doc. RNDr. Jiří Tomáš, Dr. (člen)
doc. Mgr. et Mgr. Aleš Návrat, Ph.D. (člen)
Mariapia Palombaro (člen)
Gennaro Ciampa (člen)
Matteo Colangeli (člen)
Carmela Scalone (člen)
Date of acceptance
2024-10-04
Defence
The student presented her master's thesis on the topic: BDF and BBDF for solving Ordinary Differential Equations. After the presentation, the supervisor's and the opponent's reviews were read. The student has suitably answered all the opponent's and committee members' questions.
Result of defence
práce byla úspěšně obhájena
Document licence
Standardní licenční smlouva - přístup k plnému textu bez omezení