An extension of the Legendre-Galerkin method for solving sixth-order differential equations with variable polynomial coefficients
type: Item
instance of: scholarly article
title: An extension of the Legendre-Galerkin method for solving sixth-order differential equations with variable polynomial coefficients
zbMATH Open document ID: 1264.65121
DOI: 10.1155/2012/896575
author: A. H. Bhrawy
author: S. I. El-Soubhy
author: A. S. Alofi
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We extend the application of Legendre-Galerkin algorithms for sixth-order elliptic problems with constant coefficients to sixth-order elliptic equations with variable polynomial coefficients. The complexities of the algorithm are \(O(N)\) operations for a one-dimensional domain with (\(N - 5\)) unknowns. An efficient and accurate direct solution for algorithms based on the Legendre-Galerkin approximations developed for the two-dimensional sixth-order elliptic equations with variable coefficients relies upon a tensor product process. The proposed Legendre-Galerkin method for solving variable coefficients problem is more efficient than pseudospectral method. Numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques.
Mathematics Subject Classification ID: 65L60
zbMATH DE Number: 6173673
Wikidata QID: Q58912625
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/896575
OpenAlex ID: W2072068641
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description: scientific article; zbMATH DE number 6173673