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- H. M. Ahmed, S. I. El-Soubhy
- Applied Mathematics and Computation
- 2008

- A. H. Bhrawy, S. I. El-Soubhy
- Applied Mathematics and Computation
- 2010

Efficiently direct solvers based on the Jacobi–Galerkin method for the integrated forms of second-order elliptic equations in one and two space variables are presented. They are based on appropriate base functions for the Galerkin formulation which lead to discrete systems with specially structured matrices that can be efficiently inverted. The homogeneous… (More)

and Applied Analysis 3 2. Preliminaries Let w α,β x 1 − x α 1 x β be a weight function in the usual sense for α, β > −1. The set of Jacobi polynomials {P α,β k x } k 0 forms a complete L 2 w α,β −1, 1 -orthogonal system, and ∥ ∥ ∥P α,β k ∥ ∥ ∥ 2 w α,β h α,β k 2 β 1Γ k α 1 Γ ( k β 1 ) ( 2k α β 1 ) Γ k 1 Γ ( k α β 1 ) . 2.1 Here, L2 w α,β −1, 1 is a weighted… (More)

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