Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem

M. El-Kady; M.A.Attia; F. Ragab

doi:10.12816/0004797

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JE&AS. 2014; 1(1): 37-43

doi: 10.12816/0004797

Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem

M. El-Kady, M.A.Attia, F. Ragab.

Abstract
In this paper,we applied successive ultraspherical integration matrices, which are used for the numerical solution of fourth order linear boundary value problem arising in bending of a rectangular beam on elastic foundation. This method is used to approximate for the highest-order derivative and generating approximations to the lower-order derivatives through integration of the highest-order derivative. We can then use the produced equations in the form of algebraic system and hence it is converted to nonlinear programming. Numerical examples illustratedthe accuracy and efficiency of the proposed method

Key words: Ultraspherical polynomials; integration matrices;beam bending boundary value problem.

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How to Cite this Article

Pubmed Style

El-Kady M, M.A.Attia , Ragab F. Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem. JE&AS. 2014; 1(1): 37-43. doi:10.12816/0004797

Web Style

El-Kady M, M.A.Attia , Ragab F. Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem. https://jecasmu.org/?mno=91598 [Access: January 03, 2024]. doi:10.12816/0004797

AMA (American Medical Association) Style

El-Kady M, M.A.Attia , Ragab F. Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem. JE&AS. 2014; 1(1): 37-43. doi:10.12816/0004797

Vancouver/ICMJE Style

El-Kady M, M.A.Attia , Ragab F. Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem. JE&AS. (2014), [cited January 03, 2024]; 1(1): 37-43. doi:10.12816/0004797

Harvard Style

El-Kady, M., M.A.Attia, . & Ragab, . F. (2014) Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem. JE&AS, 1 (1), 37-43. doi:10.12816/0004797

Turabian Style

El-Kady, M., M.A.Attia, and F. Ragab. 2014. Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem. Journal of Engineering and Applied Sciences-JE&AS, 1 (1), 37-43. doi:10.12816/0004797

Chicago Style

El-Kady, M., M.A.Attia, and F. Ragab. "Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem." Journal of Engineering and Applied Sciences-JE&AS 1 (2014), 37-43. doi:10.12816/0004797

MLA (The Modern Language Association) Style

El-Kady, M., M.A.Attia, and F. Ragab. "Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem." Journal of Engineering and Applied Sciences-JE&AS 1.1 (2014), 37-43. Print. doi:10.12816/0004797

APA (American Psychological Association) Style

El-Kady, M., M.A.Attia, . & Ragab, . F. (2014) Ultraspherical Integration Method for Solving Beam Bending Boundary Value Problem. Journal of Engineering and Applied Sciences-JE&AS, 1 (1), 37-43. doi:10.12816/0004797