The purpose of this chapter is to provide a survey of our book by placing what we have to
say in a historical context. We obviously cannot give a complete account of inverse …

This book combines theory, applications, and numerical methods, and covers each of these
fields with the same weight. In order to make the book accessible to mathematicians …

These notes provide an introduction to the theory of spherical harmonics in an arbitrary
dimension as well as an overview of classical and recent results on some aspects of the …

In this article we describe recent progress on the design, analysis and implementation of
hybrid numerical-asymptotic boundary integral methods for boundary value problems for the …

In this paper, a Jacobi-collocation spectral method is developed for Volterra integral
equations of the second kind with a weakly singular kernel. We use some function …

Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we
extend the study of Veerapaneni et al.[SK Veerapaneni, D. Gueyffier, G. Biros, D. Zorin, A …

We propose and analyze a spectral Jacobi-collocation approximation for the linear Volterra
integral equations (VIEs) of the second kind with weakly singular kernels. In this work, we …

In this paper, we propose and analyze a spectral Jacobi-collocation method for the
numerical solution of general linear fractional integro-differential equations. The fractional …

We present a high-order boundary integral equation solver for 3D elliptic boundary value
problems on domains with smooth boundaries. We use Nyström's method for discretization …

In this work we describe, implement and analyse in detail a high-order fully discrete spectral
algorithm for solving the Helmholtz equation exterior to a bounded (sound-soft, sound-hard …