Generalized Jacobi-Gauss-Lobatto interpolation

Abstract

We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order problems. We establish some results on these interpolations in non-uniformly weighted Sobolev spaces, which serve as the basic tools in analysis of numerical quadratures and various numerical methods of differential and integral equations.

Keywords

Generalized Jacobi-Gauss-Lobatto interpolation / pseudospectral method / non-uniformly weighted Sobolev space

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