Numerical investigation of dynamic Euler-Bernoulli equation via 3-Scale Haar wavelet collocation method

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dc.authoridEsen, Alaattin/0000-0002-7927-5941
dc.authoridOruç, Ömer/0000-0002-6655-3543
dc.authoridBulut, Fatih/0000-0001-6603-2468
dc.authorwosidEsen, Alaattin/ABE-5694-2021
dc.authorwosidOruç, Ömer/R-2813-2019
dc.authorwosidBulut, Fatih/F-7201-2013
dc.contributor.authorOruc, Omer
dc.contributor.authorEsen, Alaattin
dc.contributor.authorBulut, Fatih
dc.date.accessioned2024-08-04T20:10:04Z
dc.date.available2024-08-04T20:10:04Z
dc.date.issued2021
dc.departmentİnönü Üniversitesien_US
dc.description.abstractIn this study, we analyze the performance of a numerical scheme based on 3-scale Haar wavelets for dynamic Euler-Bernoulli equation, which is a fourth order time dependent partial differential equation. This type of equations governs the behaviour of a vibrating beam and have many applications in elasticity. For its solution, we first rewrite the fourth order time dependent partial differential equation as a system of partial differential equations by introducing a new variable, and then use finite difference approximations to discretize in time, as well as 3-scale Haar wavelets to discretize in space. By doing so, we obtain a system of algebraic equations whose solution gives wavelet coefficients for constructing the numerical solution of the partial differential equation. To test the accuracy and reliability of the numerical scheme based on 3-scale Haar wavelets, we apply it to five test problems including variable and constant coefficient, as well as homogeneous and non-homogeneous partial differential equations. The obtained results are compared wherever possible with those from previous studies. Numerical results are tabulated and depicted graphically. In the applications of the proposed method, we achieve high accuracy even with small number of collocation points.en_US
dc.identifier.doi10.15672/hujms.610834
dc.identifier.endpage179en_US
dc.identifier.issn2651-477X
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85101135074en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage159en_US
dc.identifier.trdizinid492645en_US
dc.identifier.urihttps://doi.org/10.15672/hujms.610834
dc.identifier.urihttps://search.trdizin.gov.tr/yayin/detay/492645
dc.identifier.urihttps://hdl.handle.net/11616/92584
dc.identifier.volume50en_US
dc.identifier.wosWOS:000640068900015en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakTR-Dizinen_US
dc.language.isoenen_US
dc.publisherHacettepe Univ, Fac Scien_US
dc.relation.ispartofHacettepe Journal of Mathematics and Statisticsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subject3-Scale Haar waveletsen_US
dc.subjectvibrating beamen_US
dc.subjectdynamic Euler-Bernoulli equationen_US
dc.titleNumerical investigation of dynamic Euler-Bernoulli equation via 3-Scale Haar wavelet collocation methoden_US
dc.typeArticleen_US

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