Spectral Methods

Abstract

Due to a technical error the caption of Figure 1.6 on page 29 and the content of pages 311 and 312 were reproduced in non-final form. Please find the corrected pages below. On pages 311 and 312 the changes are highlighted in red.

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

“…In this paper we deal with multivariate polynomial inequalities of Markov type and Nikolskii type. The results proposed can find possible applications, among others, in the fields of polynomial approximation techniques for aleatory functions [6,18,14], for parametric and stochastic partial differential equations [17,4,14], spectral methods [3] and high-order finite element methods [20].…”

Least-Squares Spectral Method for the solution of a fractional advection–dispersion equation

“…(4), (11) and (12), are not performed analytically but approximated by quadrature rules. More detail on high order polynomial approximations and quadratures can be found in [60,Chapter 2]. In the general case a quadrature can approximate the integral of the product of a given integrand function f ðnÞ times a weight function WðnÞ over a one-dimensional integration domain H as a sum of the values of the integrand function evaluated in the quadrature points n a multiplied by appropriate quadrature weights x a as…”

Tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the oil palm frond as a promising source of xylose

“…variational iteration method [18], homotopy perturbation method [19], Waveform relaxation methods [20] and collocation method [21,22]. Expression of a function in terms of a series expansion exploiting orthogonal polynomials is an essential concept in the approximation theory and constitutes the foundation for solving differential equations [23]. Recently, a considerable attention was given to apply the orthogonal functions for solving fractional differential equations [24,25,26,27,28].…”