Open AccessEfficient Solutions of Multidimensional Sixth‐Order Boundary Value Problems Using Symmetric Generalized Jacobi‐Galerkin Method
Author(s) -
E. H. Doha,
W. M. AbdElhameed
Publication year - 2012
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2012/749370
Subject(s) - mathematics , jacobi method , boundary value problem , galerkin method , dimension (graph theory) , order (exchange) , matrix (chemical analysis) , spectral method , jacobi polynomials , algorithm , mathematical analysis , finite element method , orthogonal polynomials , pure mathematics , physics , materials science , finance , economics , composite material , thermodynamics
This paper presents some efficient spectral algorithms for solving linear sixth-ordertwo-point boundary value problems in one dimension based on the application of theGalerkin method. The proposed algorithms are extended to solve the two-dimensionalsixth-order differential equations. A family of symmetric generalized Jacobi polynomialsis introduced and used as basic functions. The algorithms lead to linear systems withspecially structured matrices that can be efficiently inverted. The various matrix systemsresulting from the proposed algorithms are carefully investigated, especially theircondition numbers and their complexities. These algorithms are extensions to some ofthe algorithms proposed by Doha and Abd-Elhameed (2002) and Doha and Bhrawy (2008) for second- andfourth-order elliptic equations, respectively. Three numerical results are presentedto demonstrate the efficiency and the applicability of the proposed algorithms
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