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http://dspace.univ-guelma.dz/jspui/handle/123456789/14372Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | SEDKA, Ilyes | - |
| dc.date.accessioned | 2023-07-10T08:17:55Z | - |
| dc.date.available | 2023-07-10T08:17:55Z | - |
| dc.date.issued | 2023-07-08 | - |
| dc.identifier.uri | http://dspace.univ-guelma.dz/jspui/handle/123456789/14372 | - |
| dc.description.abstract | Theobjectiveofthisthesisistoimprovenumericallinearizationtechniquesforsolvingsystemsofnonlinearintegralequations,whichplayacrucialroleinmodelingvariousproblemsacrossdomainssuchasphysics,biology,andmachinelearning.Thestudyfocuses on Banach spaces.Traditionally, most methods involve discretizing the problemfirstandthenproceedingwiththelinearizationprocesstosolvenonlinearfunctionalproblems.However,weproposeanovelapproachthatreversesthisorder,startingwiththelinearizationprocessusingNewton’siterativemethod,andthendiscretizingtheiterativelinearsystemobtainedfromthefirstphase.Weapplythisapproachtosolveavarietyofproblems,startingwithasystemofnonlinearFredholmintegralequationsofthesecondkindwithregularkernels,usingtheNyströmmethodfordiscretization. Additionally,weintroduceanewschemewithadoublediscretizationprocessthatutilizestheKantorovichprojectionmethodtoapproximatesolutionsfornonlinearfunctionalequations,specificallynonlinearintegro-differentialequationsofthesecondkind.Finally,weapplyourapproachtosolveasystemofnonlinearintegro-differentialequationswithaweaklysingularkernel,estimatingallintegralswithweaklysingularkernelsusingproductintegrationrules.Wehaveprovidednecessaryconditionsforeachapplicationtoensuretheconvergenceofourmethods. | en_US |
| dc.language.iso | en | en_US |
| dc.subject | SystemofnonlinearFredholmintegralequations,Systemofnonlinearintegro-differentialequations,Kantorovichprojection,NewtonIterativeMethod,Nystömquadraturemethod,Productintegrationprocess,Linearization-Discretization MathematicsSubjectClassification:45B05,47G20,45F05,65R10,65F10,64R20 | en_US |
| dc.title | Généralisation des techniques de linéarisation pour approcher les systèmes d'équations intégrales non linéaires | en_US |
| dc.type | Thesis | en_US |
| Appears in Collections: | Thèses de Doctorat | |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| THESE DOCTORAT SEDKA ILYES.pdf | 2,05 MB | Adobe PDF | View/Open |
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