University Sétif 1 FERHAT ABBAS Faculty of Sciences
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Titre : Investigation Of Nonlinear Integro-Differential Equations Using Numerical Technique Type de document : document électronique Auteurs : Imene Benchiker, Auteur ; yasmina Kadri, Directeur de thèse Editeur : Sétif:UFA1 Année de publication : 2025 Importance : 1 vol (32 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Integral-differential equation
Laplace transform
Homotopy perturbation method
Exact solutionIndex. décimale : 510-Mathématique Résumé : Abstract :
Integro-differential equations are among the most important differential equations that have appeared in various scientific fields such as physics, chemistry, viscoelasticity, medicine, control theory, and others. This work aims to present the Laplace homotopy perturbation method for solving nonlinear integro-differential equations. The applicability and effectiveness of this method have been demonstrated through its application to practical examples.
Note de contenu : Tableofcontents
Introductioniii
1 Generalitiesonintegro-di¤erentialequations1
1.1Integro-di¤erentialequations........................... 1
1.2Classi…cationofintegro-di¤erentialequations................ 2
1.2.1Fredholmintegro-di¤erentialequation................ 2
1.2.2Velterraintegro-di¤erentialequation.................. 3
1.2.3Volterra-Fredholmintegro-di¤erentialequation............. 3
1.3Propertiesofintegro-di¤erentialequation.................... 4
1.3.1Firstandsecondtype........................... 4
1.3.2Homogeneityandlinearity........................ 4
1.3.3Singularity................................. 5
1.3.4Orderofanintegro-di¤erentialequation................ 5
1.3.5Existenceanduniquenesstheorems................... 5
1.3.6Fixedpointtheorem........................... 5
1.3.7ExistenceanduniquenesstheoremforthesolutionofVolterraintegro-
di¤erentialequation............................ 6
1.3.8ExistenceanduniquenessofthesolutionoftheFredholmintegro-
di¤erentialequation............................ 8
2 Onthesolutionsofintegro-di¤erentialequations11
2.1Laplacetransformmethod(LTM)........................ 11
2.1.1DeÂ…nitionandexistence......................... 11
2.1.2Laplacetransformofelementaryfunctions............... 13
2.1.3PropertiesoftheLaplacetransform................... 13
2.2Homotopyperturbationmethod(HPM)..................... 15
2.2.1DescriptionoftheMethod........................ 16
2.2.2Convergenceanalysis........................... 17
3 ProcedureoftheLaplacehomotopyperturbationmethodfornonlinear
integro-di¤erentialequations25
3.1MethodologyoftheLHPM............................ 25
3.2Illustrativeexamples............................... 27
Conclusion32Côte titre : MAM/0787 Investigation Of Nonlinear Integro-Differential Equations Using Numerical Technique [document électronique] / Imene Benchiker, Auteur ; yasmina Kadri, Directeur de thèse . - [S.l.] : Sétif:UFA1, 2025 . - 1 vol (32 f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Integral-differential equation
Laplace transform
Homotopy perturbation method
Exact solutionIndex. décimale : 510-Mathématique Résumé : Abstract :
Integro-differential equations are among the most important differential equations that have appeared in various scientific fields such as physics, chemistry, viscoelasticity, medicine, control theory, and others. This work aims to present the Laplace homotopy perturbation method for solving nonlinear integro-differential equations. The applicability and effectiveness of this method have been demonstrated through its application to practical examples.
Note de contenu : Tableofcontents
Introductioniii
1 Generalitiesonintegro-di¤erentialequations1
1.1Integro-di¤erentialequations........................... 1
1.2Classi…cationofintegro-di¤erentialequations................ 2
1.2.1Fredholmintegro-di¤erentialequation................ 2
1.2.2Velterraintegro-di¤erentialequation.................. 3
1.2.3Volterra-Fredholmintegro-di¤erentialequation............. 3
1.3Propertiesofintegro-di¤erentialequation.................... 4
1.3.1Firstandsecondtype........................... 4
1.3.2Homogeneityandlinearity........................ 4
1.3.3Singularity................................. 5
1.3.4Orderofanintegro-di¤erentialequation................ 5
1.3.5Existenceanduniquenesstheorems................... 5
1.3.6Fixedpointtheorem........................... 5
1.3.7ExistenceanduniquenesstheoremforthesolutionofVolterraintegro-
di¤erentialequation............................ 6
1.3.8ExistenceanduniquenessofthesolutionoftheFredholmintegro-
di¤erentialequation............................ 8
2 Onthesolutionsofintegro-di¤erentialequations11
2.1Laplacetransformmethod(LTM)........................ 11
2.1.1DeÂ…nitionandexistence......................... 11
2.1.2Laplacetransformofelementaryfunctions............... 13
2.1.3PropertiesoftheLaplacetransform................... 13
2.2Homotopyperturbationmethod(HPM)..................... 15
2.2.1DescriptionoftheMethod........................ 16
2.2.2Convergenceanalysis........................... 17
3 ProcedureoftheLaplacehomotopyperturbationmethodfornonlinear
integro-di¤erentialequations25
3.1MethodologyoftheLHPM............................ 25
3.2Illustrativeexamples............................... 27
Conclusion32Côte titre : MAM/0787 Exemplaires (1)
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