We derive explicitly the weights and the nodes of the generalized Gauss-Radau and Gauss-Lobatto quadratures with Jacobi weight functions. AMS subject classification: 65D32, 65D30, 41A55.

The method of moments (MOM) is a statistically based alternative to sectional and modal methods for aerosol simulation. The MOM is highly efficient as the aerosol distribution is represented by its lower-order moments and only these, not the full distribution itself, are tracked during simulation. Quadrature is introduced to close the moment equations under very general growth laws and to compu...

In this paper, we develop two piecewise polynomial methods for the numerical evaluation of Cauchy Principal Value integrals of oscillatory kind. The two piecewisepolynomial quadratures are compact, easy to implement, and are numerically stable. Two numerical examples are presented to illustrate the two rules developed, The convergence of the two schemes is proved and some error bounds obtai...

We propose a Riesz transform approach to the demodulation of digital holograms. The Riesz transform is a higher-dimensional extension of the Hilbert transform and is steerable to a desired orientation. Accurate demodulation of the hologram requires a reliable methodology by which quadrature-phase functions (or simply, quadratures) can be constructed. The Riesz transform, by itself, does not yie...

For a system of ordinary differential equations (ODEs) or, more generally, an involutive distribution vector fields, the problem its integration is considered. Among many approaches to this problem, solvable structures provide systematic procedure via Pfaffian that are integrable by quadratures. In paper general than (named cinf-structures) The symmetry condition in concept structure weakened f...

Accurate angular quadratures are crucial for the numerical solution of three-dimensional (3D) radiative transfer problems, especially when spectral line polarisation produced by scattering anisotropic radiation is included. There two requirements obtaining an optimal quadrature and they difficult to satisfy simultaneously: high accuracy short computing time. By imposing certain symmetries, we w...

It is shown that the Maxwell's equations for surface electromagnetic TM waves, propagating along the plane boundary between two nonlinear dielectrics with arbitrary diagonal tensor of dielectric permittivity, depending on |E|, can be integrated in quadratures.