An Extension of the Legendre-Galerkin Method for Solving Sixth-Order Differential Equations with Variable Polynomial Coefficients
Joint Authors
Bhrawy, Ali H.
Alofi, Abdulaziz
El-Soubhy, S. I.
Source
Mathematical Problems in Engineering
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-22
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Bhrawy, Ali H.& Alofi, Abdulaziz& El-Soubhy, S. I.. 2012. An Extension of the Legendre-Galerkin Method for Solving Sixth-Order Differential Equations with Variable Polynomial Coefficients. Mathematical Problems in Engineering،Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-1002057
Modern Language Association (MLA)
Bhrawy, Ali H.…[et al.]. An Extension of the Legendre-Galerkin Method for Solving Sixth-Order Differential Equations with Variable Polynomial Coefficients. Mathematical Problems in Engineering No. 2012 (2012), pp.1-13.
https://search.emarefa.net/detail/BIM-1002057
American Medical Association (AMA)
Bhrawy, Ali H.& Alofi, Abdulaziz& El-Soubhy, S. I.. An Extension of the Legendre-Galerkin Method for Solving Sixth-Order Differential Equations with Variable Polynomial Coefficients. Mathematical Problems in Engineering. 2012. Vol. 2012, no. 2012, pp.1-13.
https://search.emarefa.net/detail/BIM-1002057
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1002057