Optimal pointwise error estimates for piecewise functions expanded with Laguerre polynomials

Abstract

This paper focuses on pointwise error estimates for piecewise functions expanded in the form of Laguerre polynomial series. By utilizing the reproducing kernel of Laguerre polynomials, we derive an explicit pointwise error formula, which enables the estimation of convergence orders of pointwise values for piecewise functions by using the Hilb-type formula and generalized van der Corput-type Lemmas. The presented convergence analyses illustrate that the piecewise functions exhibit local superconvergence away from the singular points. Plenty of numerical experiments are carried out to validate the accuracy of these theoretical results.