Investigation of an exact solution of a mixed boundary value problem using the residue method

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dc.contributor.authorSinsoysal, Bahaddin
dc.contributor.authorRasulov, Mahir A.
dc.date.accessioned2025-02-09T14:32:53Z
dc.date.available2025-02-09T14:32:53Z
dc.date.issued2024
dc.departmentFakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
dc.description.abstractIn this study, a finite differences method is proposed for solving a mixed problem, which represents phenomena in hydrodynamics. To evaluate the approximate solution of the problem, its analytical solution is also constructed by the residue method developed by M.L. Rasulov, which is applied to find the solution of the partial differential equations containing time-dependent derivatives at boundary conditions. The formula for expansion of an arbitrary function in a series of residues of the solution of the corresponding spectral problem is used to show that the solution of the mixed boundary-value problem can be represented by the given residue formula. The use of the residual method gives an exact solution for the mixed boundary value problem, represented as a rapidly decreasing series. The derived formula makes it possible to formally establish both the existence and the uniqueness of the solution. Moreover, the derived formula provides a framework for evaluation, allowing a comparative analysis between the exact solution and the numerical approach.
dc.identifier.doi10.61150/ijonfest.2024020203
dc.identifier.endpage105
dc.identifier.issn3023-4379
dc.identifier.issue2
dc.identifier.startpage98
dc.identifier.urihttps://hdl.handle.net/11501/1645
dc.identifier.urihttps://doi.org/10.61150/ijonfest.2024020203
dc.identifier.volume2
dc.institutionauthorSinsoysal, Bahaddin
dc.institutionauthorid0000-0003-2926-2744
dc.language.isoen
dc.publisherIstanbul Gedik University
dc.relation.ispartofInternational Journal of New Findings in Engineering, Science and Technology
dc.relation.publicationcategoryMakale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_DergiPark_20250209
dc.subjectResidue Method
dc.subjectResidue Representation of the Solution
dc.subjectExpansion Formula
dc.subjectBoundary Condition With Higher Order Derivative
dc.titleInvestigation of an exact solution of a mixed boundary value problem using the residue method
dc.typeArticle

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International Journal of New Findings in Engineering, Science and Technology