We survey some recent applications of radial basis functions (rbfs) for the BEM and related
algorithms such as the method of fundamental solutions. Among these are the use of …

Completely revised text focuses on use of spectral methods to solve boundary value,
eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational …

Radial basis function methods are modern ways to approximate multivariate functions,
especially in the absence of grid data. They have been known, tested and analysed for …

Spherical t-designs on 𝕊 d⊂ ℝ d+ 1 S^ d ⊂ R^ d+ 1 provide N nodes for an equal weight
numerical integration rule which is exact for all spherical polynomials of degree at most t …

This chapter is concerned with numerical integration over the unit sphere $${\mathbb
{S}}^{2}\subset {\mathbb {R}}^{3} $$. We first discuss basic facts about numerical integration …

This paper explores the quality of polynomial interpolation approximations over the sphere S
r− 1⊂ R r in the uniform norm, principally for r= 3. Reimer [17] has shown there exist …

Multivariate polynomials are a main tool in approximation. The book begins with an
introduction to the general theory by presenting the most important facts on multivariate …

In this paper we present a mesh-free approach to numerically solving a class of second
order time dependent partial differential equations which include equations of parabolic …

This paper considers the problem of constructive approximation of a continuous function on
the unit sphere Sr− 1⊆ R r by a spherical polynomial from the space P n of all spherical …

In this paper we describe and analyse a class of spectral methods, based on spherical
polynomial approximation, for second-kind weakly singular boundary integral equations …