Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
Journal of Approximation Theory
Second order Jacobi approximation with applications to fourth-order differential equations
Applied Numerical Mathematics
Mixed Jacobi-spherical harmonic spectral method for Navier--Stokes equations
Applied Numerical Mathematics
Second order Jacobi approximation with applications to fourth-order differential equations
Applied Numerical Mathematics
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Gegenbauer approximation in certain Hilbert spaces is investigated. Several weighted inverse inequalities and Poincaré inequalities are obtained. Some approximation results are given. Singular differential equations are approximated by using Gegenbauer polynomials. This method keeps the spectral accuracy. The main idea and techniques used in this paper are also applicable to some singular problems in multiple-dimensional spaces.