University Sétif 1 FERHAT ABBAS Faculty of Sciences
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Titre : Meta-heuristic algorithms for solving ordinary differential equations Type de document : texte imprimé Auteurs : Houda Boulekfouf, Auteur ; Houda Chettout ; Ihcene Naas, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2024 Importance : 1 vol (39 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Differential equations
Approximate methods
Meta-heuristic algorithms
Optimization problems
Gravity search algorithms
RL.Index. décimale : 510-Mathématique Résumé :
When analytical methods are unable to solve differential equations, approximation methods are considered the best solution. Among the approximation methods, the meta-heuristic algorithm that was devised by observing phenomena that occur in nature has proven its ability to find near-optimal solutions to real-valued numerical problems. This work focuses on solving initial value problems by transforming them into an optimization problem by creating an objective function that includes both the initial value problem and its initial conditions. We used one of the most famous optimization methods: the gravity search algorithm, which is based on the principles of Newtonian gravity and the laws of motion. In the scientific work, we focus on the application of this algorithm in the field of electronics and electrical engineering when we solve the problem of the initial value resulting from an RL circuit.Note de contenu :
Sommaire
1 DIFFERENTIALEQUATIONS 1
1.1 Introduction . .................................. 1
1.2 Differentialequations . ............................. 2
1.2.1 Ordinarydifferentialequation . ................... 2
1.2.2 Taxonomyofdifferentialequations . ................. 3
1.3 TaxonomyofmethodsforsolvingDEs . ................... 4
1.3.1 Numericalmethodsforsolvingdifferentialequations . ...... 5
1.4 Limitationoftheclassicmethod . ....................... 10
2 Meta-heuristicsalgorithmforsolvingODEs 12
2.1 Introduction . .................................. 12
2.2 Optimizationproblems . ............................ 13
2.2.1 Typesofoptimizationmethods . ................... 14
2.3 Meta-heuristicalgorithms . .......................... 15
2.3.1 Meta-heuristicbackground . ..................... 15
2.3.2 Classificationofmeta-heuristicalgorithms . ............ 16
2.4 Meta-heuristicforsolvingODEs . ...................... 18
2.4.1 Statoftheart . ............................. 18
2.4.2 TransformationofanODEsintooptimizationproblem . ..... 20
3 SolvingRLCircuitProblemusingGSAalgorithm 23
3.1 Introduction . .................................. 23
3.2 Anoverviewofthegravitationalsearchalgorithm . ............ 24
3.2.1 FlowChartofGSAalgorithm . .................... 27
3.3 RLCircuitProblem . .............................. 28
3.3.1 TheStepResponseofanRLCircuit . ................ 28
3.4 RLcircuitintooptimizationproblem . ................... 29
3.5 Simulationandnumericalresult . ...................... 30
3.5.1 ParametersadoptedofGSA . ..................... 30
3.5.2 Application . .............................. 30
3.5.3 Resultsanddiscussion . ........................ 31Côte titre : MAM/0728 Meta-heuristic algorithms for solving ordinary differential equations [texte imprimé] / Houda Boulekfouf, Auteur ; Houda Chettout ; Ihcene Naas, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (39 f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Differential equations
Approximate methods
Meta-heuristic algorithms
Optimization problems
Gravity search algorithms
RL.Index. décimale : 510-Mathématique Résumé :
When analytical methods are unable to solve differential equations, approximation methods are considered the best solution. Among the approximation methods, the meta-heuristic algorithm that was devised by observing phenomena that occur in nature has proven its ability to find near-optimal solutions to real-valued numerical problems. This work focuses on solving initial value problems by transforming them into an optimization problem by creating an objective function that includes both the initial value problem and its initial conditions. We used one of the most famous optimization methods: the gravity search algorithm, which is based on the principles of Newtonian gravity and the laws of motion. In the scientific work, we focus on the application of this algorithm in the field of electronics and electrical engineering when we solve the problem of the initial value resulting from an RL circuit.Note de contenu :
Sommaire
1 DIFFERENTIALEQUATIONS 1
1.1 Introduction . .................................. 1
1.2 Differentialequations . ............................. 2
1.2.1 Ordinarydifferentialequation . ................... 2
1.2.2 Taxonomyofdifferentialequations . ................. 3
1.3 TaxonomyofmethodsforsolvingDEs . ................... 4
1.3.1 Numericalmethodsforsolvingdifferentialequations . ...... 5
1.4 Limitationoftheclassicmethod . ....................... 10
2 Meta-heuristicsalgorithmforsolvingODEs 12
2.1 Introduction . .................................. 12
2.2 Optimizationproblems . ............................ 13
2.2.1 Typesofoptimizationmethods . ................... 14
2.3 Meta-heuristicalgorithms . .......................... 15
2.3.1 Meta-heuristicbackground . ..................... 15
2.3.2 Classificationofmeta-heuristicalgorithms . ............ 16
2.4 Meta-heuristicforsolvingODEs . ...................... 18
2.4.1 Statoftheart . ............................. 18
2.4.2 TransformationofanODEsintooptimizationproblem . ..... 20
3 SolvingRLCircuitProblemusingGSAalgorithm 23
3.1 Introduction . .................................. 23
3.2 Anoverviewofthegravitationalsearchalgorithm . ............ 24
3.2.1 FlowChartofGSAalgorithm . .................... 27
3.3 RLCircuitProblem . .............................. 28
3.3.1 TheStepResponseofanRLCircuit . ................ 28
3.4 RLcircuitintooptimizationproblem . ................... 29
3.5 Simulationandnumericalresult . ...................... 30
3.5.1 ParametersadoptedofGSA . ..................... 30
3.5.2 Application . .............................. 30
3.5.3 Resultsanddiscussion . ........................ 31Côte titre : MAM/0728 Exemplaires (1)
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