An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain

We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.

Partial Quasi-Bilateral Generating Function Involving some Special Functions

A group-theoretic method of obtaining more general class of generating functions from a given class of partial quasi-bilateral generating functions involving Hermite, Laguerre and Gegenbaur polynomials are discussed.

Problems and Theorems in the Theory of Multiplier Sequences

The purpose of this paper is (1) to highlight some recent and heretofore unpublished results in the theory of multiplier sequences and (2) to survey some open problems in this area of research. For the sake of clarity of exposition, we have grouped the problems in three subsections, although several of the problems are interrelated. For the reader’s convenience, we have included the pertinent definitions, cited references and related results, and in several instances, elucidated the problems by examples.

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

A Unified Group-Theoretic Method on Improper Partial Semi-Bilateral Generating Functions

2000 Mathematics Subject Classification: 33A65, 33C20.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Temperature-averaged and total free-free Gaunt factors for κ and Maxwellian distributions of electrons

Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by κ-distributions. The free-free spectrum and radiative losses depend on the temperature-averaged (over the electrons distribution) and total Gaunt factors, respectively. Thus, there is a need to calculate and make available these factors to be used by any software that deals with plasma emission. Methods. We recalculated the free-free Gaunt factor for a wide range of energies and frequencies using hypergeometric functions of complex arguments and the Clenshaw recurrence formula technique combined with approximations whenever the difference between the initial and final electron energies is smaller than 10−10 in units of z2Ry. We used double and quadruple precisions. The temperature- averaged and total Gaunt factors calculations make use of the Gauss-Laguerre integration with 128 nodes. Results. The temperature-averaged and total Gaunt factors depend on the κ parameter, which shows increasing deviations (with respect to the results obtained with the use of the Maxwellian distribution) with decreasing κ. Tables of these Gaunt factors are provided.