A fourth order accurate approximation of the solution of Laplace's equation on a rectangle using the two-stage difference method

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dc.contributor.authorSarıkaya, Hediye
dc.date.accessioned2024-07-12T20:47:13Z
dc.date.available2024-07-12T20:47:13Z
dc.date.issued2021en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractIn this paper, two stage difference method is presented to solve the Dirichlet problem for the Laplace equation on rectangle. In the first stage, the sum of the pure fourth order derivatives of the required solution is approximated on a square grid. Then, by using the quantities that are determined in the first stage, the system of difference equations which approximates the Dirichlet problem, is computed during the second stage. The difference equations found in the stages are formulated by using the 5?point averaging operator. Due to these facts that, the boundary values are continuous and sixth times differentiable at the edges of the rectangle, the derivatives of them satisfy Holder ¨ condition and at the end, their second and fourth order derivatives meet the matching condition implied by the Laplace equation. We proved that the difference solution of the Dirichlet problem is uniform convergent with the order O(h4), where h denotes the mesh size.en_US
dc.identifier.citationSarıkaya, H. (2021). A fourth order accurate approximation of the solution of Laplace's equation on a rectangle using the two-stage difference method. Fourth International Conference of Mathematical Sciences, Maltepe Üniversitesi. s. 1-5.en_US
dc.identifier.endpage5en_US
dc.identifier.isbn978-0-7354-4078-4
dc.identifier.startpage1en_US
dc.identifier.urihttps://aip.scitation.org/doi/10.1063/5.0042237
dc.identifier.urihttps://hdl.handle.net/20.500.12415/1953
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofFourth International Conference of Mathematical Sciencesen_US
dc.relation.isversionof10.1063/5.0042237en_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY07373
dc.subjectNumerical solution to the Laplace equationen_US
dc.subjectconvergence of difference solutionsen_US
dc.subjecterror estimationsen_US
dc.subjectLaplace’s equation on rectangleen_US
dc.titleA fourth order accurate approximation of the solution of Laplace's equation on a rectangle using the two-stage difference methoden_US
dc.typeConference Object
dspace.entity.typePublication

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