Browsing by Subject "Laguerre's polynomials"

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    An hybrid numerical algorithm with error estimation for a class of functional integro-differential equations
    (Gazi Universitesi, 2016) Gürbüz B.; Sezer M.
    In this paper, a numerical algorithm based on Laguerre and Taylor polynomials is applied for solving a class of functional integro-differential equations. The considered problem is transfered to a matrix equation which corresponds to a system of linear algebraic equations by Hybrid collocation method under the mixed conditions. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments. Also, the approximate solutions are corrected by using the residual correction. © 2016, Gazi University Eti Mahallesi.All rights reserved.
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    An adaptive approach for solving fourth-order partial differential equations: algorithm and applications to engineering models
    (Springer Nature, 2022) Çayan S.; Özhan B.B.; Sezer M.
    A 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.