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Jacobi spectral Galerkin method for elliptic Neumann problems. (English) Zbl 1169.65111
This is the third paper devoted by the first two authors to the spectral Jacobi-Galerkin method. This time they apply the method to the Neumann problems for 1D and 2D elliptic equations. Their main point is to construct test and trial basis functions which produce sparse discretization matrices. Four numerical examples are carried out in order to underline the efficiency of the method.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65L10 Numerical solution of boundary value problems involving ordinary differential equations
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