Results 21 to 30 of about 147 (140)
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 In this study, an accurate and efficient numerical method based on spectral collocation is presented to solve integral equations and integrodifferential equations of n‐th order. The method is developed using compact combinations of shifted Legendre polynomials as a spectral basis and shifted Legendre–Gauss–Lobatto nodes as collocation points to ...
Zineb Laouar +3 more
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Shock and Vibration, Volume 2021, Issue 1, 2021., 2021 This study presents the multi‐stepped functionally graded carbon nanotube reinforced composite (FG‐CNTRC) plate model for the first time, and its free and forced vibration is analyzed by employing the domain decomposition method. The segmentation technique is employed to discretize the structure along the length direction.
Kwanghun Kim +6 more
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New Specific and General Linearization Formulas of Some Classes of Jacobi Polynomials
Mathematics, 2020 The main purpose of the current article is to develop new specific and general linearization formulas of some classes of Jacobi polynomials. The basic idea behind the derivation of these formulas is based on reducing the linearization coefficients which ...
Waleed Mohamed Abd-Elhameed, Afnan Ali
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A connection between ultraspherical and pseudo-ultraspherical polynomials
Journal of Mathematical Analysis and Applications, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Driver, Kathy, Muldoon, Martin E.
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AIP Advances, 2020 In this study, a unified solution method to obtain the natural frequencies of the functionally graded rectangular plate (FGRP) with general elastic restraints by using ultraspherical polynomials and the Ritz method is presented.
Kwanghun Kim +4 more
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Studies in Applied Mathematics, Volume 145, Issue 1, Page 3-35, July 2020., 2020 Abstract Sparse spectral methods for solving partial differential equations have been derived in recent years using hierarchies of classical orthogonal polynomials on intervals, disks, and triangles. In this work, we extend this methodology to a hierarchy of nonclassical orthogonal polynomials on disk slices and trapeziums.
Ben Snowball, Sheehan Olver
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Least squares approximations of power series
International Journal of Mathematics and Mathematical Sciences, 2006 The classical least squares solutions in C[−1,1] in terms of linear combinations of ultraspherical polynomials are extended in order to estimate power series on (−1,1). Approximate rates of uniform and pointwise convergence are obtained, which correspond
James Guyker
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Advances in Difference Equations, 2021 In this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods.
Mohamed Abdelhakem +3 more
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Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 In this paper, we obtain some generating matrix functions and integral representations for the extended Gauss hypergeometric matrix function EGHMF and their special cases are also given. Furthermore, a specific application for the extended Gauss hypergeometric matrix function which includes Jacobi matrix polynomials is constructed.
Fuli He +4 more
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Bilateral generating functions for a new class of generalized Legendre polynominals
International Journal of Mathematics and Mathematical Sciences, 1980 Recently Chatterjea (1) has proved a theorem to deduce a bilateral generating function for the Ultraspherical polynomials. In the present paper an attempt has been made to give a general version of Chatterjea's theorem.
A. N. Srivastava +2 more
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