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 …

Differentiation matrices are in wide use in numerical algorithms, although usually studied in
an ad hoc manner. We collect here in this review paper elementary properties of …

We consider two-dimensional scattering problems, formulated as an integral equation
defined on the boundary of the scattering obstacle. The oscillatory nature of high-frequency …

We introduce a new class of integrators for stiff ODEs as well as SDEs. Examples of
subclasses of systems that we treat are ODEs and SDEs that are sums of two terms, one of …

Based on the transformation y= g (x), some new efficient Filon-type methods for integration
of highly oscillatory function\int_a^ bf (x)\rm e^\rm i ω g (x)\rm dx with an irregular oscillator …

ADVANCES IN HEAVY TAILED RISK MODELING A cutting-edge guide for the theories,
applications, and statistical methodologies essential to heavy tailed risk modeling Focusing …

We argue that two specific wave packet families---curvelets and wave atoms---provide
powerful tools for representing linear systems of hyperbolic differential equations with …

In this paper, we present an efficient Filon-type method for the integration of systems
containing Bessel functions with exotic oscillators based on a diffeomorphism transformation …

The main functions covered in this chapter are cuspoid catastrophes ΦK (t; x); umbilic
catastrophes with codimension three Φ (E)(s, t; x), Φ (H)(s, t; x); canonical integrals ΨK (x), Ψ …

Numerical integration is encountered in all fields of numerical analysis and the engineering
sciences. By now, various efficient and accurate quadrature rules are known, for instance …