Efficiently direct solvers based on the Jacobiâ€“Galerkin method for the integrated forms of second-order elliptic equations in one and two space variables are presented. They are based on appropriateâ€¦ (More)

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. Theâ€¦ (More)

and Applied Analysis 3 2. Preliminaries Let w Î±,Î² x 1 âˆ’ x Î± 1 x Î² be a weight function in the usual sense for Î±, Î² > âˆ’1. The set of Jacobi polynomials {P Î±,Î² k x } k 0 forms a complete L 2 w Î±,Î² âˆ’1,â€¦ (More)