At present, there is still no officially accepted and extensively verified implementation of
computing the gamma difference distribution allowing unequal shape parameters. We …

Sturm-Liouville problems are abundant in the numerical treatment of scientific and
engineering problems. In the present contribution, we present an efficient and highly …

The problem of estimating single-and multi-dimensional integrals, with or without end-point
singularities, is prevalent in all fields of scientific research, and in particular in physics …

Numerical integration over the real line for analytic functions is studied. Our main focus is on
the sharpness of the error bounds. We first derive two general lower estimates for the worst …

In this work, we demonstrate the extension of quadrature approximations, built from
conformal mapping of interpolatory rules, to sparse grid quadrature in the multidimensional …

We show that the double exponential sinc-collocation method provides an efficient uniformly
accurate solution to the one-dimensional time independent Schrödinger equation for a …

The double exponential formula, or the DE formula, is a high-precision integration formula
using a change of variables called a DE transformation. However, it has a disadvantage that …

In this work, we consider several ways to overcome the challenges associated with
polynomial approximation and integration of smooth functions depending on a large number …

The double exponential formula, or DE formula, is a high-precision integration formula using
a change of variables called a DE transformation; it has the disadvantage that it is sensitive …

Model order reduction is a technique to reduce computational times of parameterized PDEs
while maintaining good accuracy of the approximated solution. Reduced basis methods …