BDF a BBDF pro řešení diferenciálních rovnic

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but.committeedoc. 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)cs
but.defenceThe 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.cs
but.jazykangličtina (English)
but.programApplied and Interdisciplinary Mathematicscs
but.resultpráce byla úspěšně obhájenacs
dc.contributor.advisorZatočilová, Jitkaen
dc.contributor.authorElusakin, Opeyemi Rachealen
dc.contributor.refereeTomášek, Petren
dc.date.created2024cs
dc.description.abstracthis 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.en
dc.description.abstracthis 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.cs
dc.description.markDcs
dc.identifier.citationELUSAKIN, O. BDF a BBDF pro řešení diferenciálních rovnic [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2024.cs
dc.identifier.other162483cs
dc.identifier.urihttp://hdl.handle.net/11012/249622
dc.language.isoencs
dc.publisherVysoké učení technické v Brně. Fakulta strojního inženýrstvícs
dc.rightsStandardní licenční smlouva - přístup k plnému textu bez omezenícs
dc.subjectStiff ordinary differential equationsen
dc.subjectimplicit linear multistep methodsen
dc.subjectstability analysisen
dc.subjectconvergenceen
dc.subjectinitial value problemsen
dc.subjectLagrange interpolation polynomialsen
dc.subjectbackward differentiation formula (BDF)en
dc.subjectblock backward differentiation formula (BBDF)en
dc.subjectstability polynomialen
dc.subjectorderen
dc.subjectMatlaben
dc.subjectStiff ordinary differential equationscs
dc.subjectimplicit linear multistep methodscs
dc.subjectstability analysiscs
dc.subjectconvergencecs
dc.subjectinitial value problemscs
dc.subjectLagrange interpolation polynomialscs
dc.subjectbackward differentiation formula (BDF)cs
dc.subjectblock backward differentiation formula (BBDF)cs
dc.subjectstability polynomialcs
dc.subjectordercs
dc.subjectMatlabcs
dc.titleBDF a BBDF pro řešení diferenciálních rovnicen
dc.title.alternativeBDF and BBDF for solving Ordinary Differential Equationscs
dc.typeTextcs
dc.type.drivermasterThesisen
dc.type.evskpdiplomová prácecs
dcterms.dateAccepted2024-10-04cs
dcterms.modified2024-10-10-07:52:17cs
eprints.affiliatedInstitution.facultyFakulta strojního inženýrstvícs
sync.item.dbid162483en
sync.item.dbtypeZPen
sync.item.insts2025.03.27 10:46:40en
sync.item.modts2025.01.15 15:59:16en
thesis.disciplinebez specializacecs
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
thesis.levelInženýrskýcs
thesis.nameIng.cs
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