An adaptive approach for solving fourth-order partial differential equations: algorithm and applications to engineering models

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dc.contributor.authorÇayan S.
dc.contributor.authorÖzhan B.B.
dc.contributor.authorSezer M.
dc.date.accessioned2024-07-22T08:03:43Z
dc.date.available2024-07-22T08:03:43Z
dc.date.issued2022
dc.description.abstractA novel numerical technique based on orthogonal Laguerre polynomials called the Laguerre matrix collocation method is proposed. The motivation of the study is to reduce the computational cost in mathematical models by adapting Laguerre polynomials directly without transforming them into the truncated Taylor polynomial basis. The new approach is suitable for solving fourth-order partial differential equations arising in physics and engineering. The algorithm and error analyses are presented in general form and applied to two physical models from solid mechanics. First, the technique is used to solve the governing equation for a plate deflection under a harmonically distributed static load. Second, the algorithm is applied to the bending model of a shear deformable plate under the harmonically distributed static load. The boundary conditions of the models are specified, and the bending responses of the models are obtained. The numerical results are compared with the exact results from the literature. The comparisons show that the new approach is suitable for numerical solutions of fourth-order partial differential equations which arise in physics and engineering. © 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.
dc.identifier.DOI-ID10.1007/s40314-022-02125-5
dc.identifier.issn22383603
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/12413
dc.language.isoEnglish
dc.publisherSpringer Nature
dc.subjectNumerical methods
dc.subjectPartial differential equations
dc.subjectPolynomials
dc.subjectAdaptive approach
dc.subjectCollocation method
dc.subjectDifferential equation algorithm
dc.subjectEngineering modelling
dc.subjectFourth order partial differential equations
dc.subjectLaguerre's polynomials
dc.subjectMatrix methods
dc.subjectNew approaches
dc.subjectPlate deflections
dc.subjectStatic loads
dc.subjectBoundary conditions
dc.titleAn adaptive approach for solving fourth-order partial differential equations: algorithm and applications to engineering models
dc.typeArticle

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