A Numerical Algorithm for a Kirchhoff‐Type Nonlinear Static Beam

Jemal Peradze

Type: Article

Publication Date: 2009-01-01

Citations: 18

DOI: https://doi.org/10.1155/2009/818269

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Abstract

A boundary value problem is posed for an integro‐differential beam equation. An approximate solution is found using the Galerkin method and the Jacobi nonlinear iteration process. A theorem on the algorithm error is proved.

Locations

Journal of Applied Mathematics - View - PDF
Project Euclid (Cornell University) - View - PDF
DOAJ (DOAJ: Directory of Open Access Journals) - View

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+	Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials	2007	E. H. Doha A. H. Bhrawy
+	Finite difference approximate solutions for the strongly damped extensible beam equations	2000	Sang‐Mok Choo S.K. Chung
+	Existence, uniqueness and uniform decay for the nonlinear beam degenerate equation with weak damping	2003	Silvano D.B. Menezes Eliane A. de Oliveira Ducival Carvalho Pereira Jorge Ferreira
+ PDF Chat	Initial-boundary value problems for an extensible beam	1973	J. M. Ball
+	Remark on the decay for damped string and beam equations	1986	Piotr Biler
+	Efficient Spectral-Galerkin Algorithms for Direct Solution of Second-Order Equations Using Ultraspherical Polynomials	2002	E. H. Doha W. M. Abd‐Elhameed
+	Low regularity global solutions for nonlinear evolution equations of Kirchhoff type	2006	Stefano Panizzi
+ PDF Chat	Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials	1994	Jie Shen
+	Existence results for a model of nonlinear beam on elastic bearings	2000	To Fu
+	Iterative Solution of Nonlinear Equations in Several Variables	2000	J. M. Ortega Werner C. Rheinboldt
+	Existence, uniqueness and asymptotic behavior for solutions of the nonlinear beam equation	1990	Ducival Carvalho Pereira
+	Stability theory for quasi-linear wave equations with linear damping	1981	R. W. Dickey
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+	Iterative solution of nonlinear equations	1994	R. D. Murphy
+ PDF Chat	The convergence of a Galerkin approximation scheme for an extensible beam	1989	Tunc Geveci I. Christie
+	Vorlesungen über mathematische physik	1877	G. Kirchhoff