V. Fack

Extended) Numerov method for computing eigenvalues of specific Schrodinger equations

Numerovs method and an extended version of it are introduced for computing eigenvalues of Schrodinger equations with potentials V(x) which are even functions with respect to x. Furthermore it is assumed that the wavefunctions tend to zero for x to +or- infinity . The derived results are compared with previously derived numerical data and with available exact values.

A finite difference approach for the calculation of perturbed oscillator energies

A simple numerical method for calculating eigenvalues and corresponding eigenvectors of the Schrodinger equation for a perturbed oscillator is described. The derived results are compared with previously derived numerical data and with available exact values.

Dynamic‐group approach to the x2+λx2/(1+gx2) potential

A modified operator method based upon the SO (2,1) dynamic group is applied to the one‐dimensional anharmonic oscillator potential V(x)=x2+λx2/(1+gx2). A tilting transformation is carried out in order to improve the rate of convergence of the algebraic perturbation series. Very accurate results are obtained for the energy eigenvalues and for the wave functions especially in the case of small g‐values.

Some finite difference methods for computing eigenvalues and eigenvectors of special two-point boundary value problems

Abstract Direct numerical integration methods will be discussed for calculating eigenvalues and eigenvectors of two-point boundary value problems involving the differential equation y″ + (a - p(x))y = 0 with p(x) = p(-x). The derived results are compared with previously derived numerical data and with available exact values.

Optimal data exchange algorithms on star graphs

Abstract Star graphs, as discussed in [1], are considered to be attractive alternatives for hypercubes. In this paper, we discuss optimal data exchange algorithms for star graphs of small dimension (n ≤ 6). In particular we study odd-distance and total exchange algorithms, using the tabular method introduced in [2]. The algorithms use no intermediate buffering of messages.

Optimal algorithms for total exchange without buffering on the hypercube

Two methods are given for constructing total exchange algorithms for hypercubic processor networks. This is done by means of bit sequences with special properties. The algorithms are optimal with respect to a given time model, need no intermediate message buffering and are local in the sense that every processor executes basically the same program.

Parallel computation of recoupling coefficients using transputers

Abstract Parallel algorithms for the computation of angular momentum recoupling coefficients are discussed. The first situation where parallelisation has a remarkable impact is for the computation of the 9- j coefficient. A parallel program in C for the numerical calculation of the 9- j coefficient is presented and compared with sequential programs in C.

The pragacz identity and a new algorithm for Littlewood-Richardson coefficients

Abstract Recently an identity relating the combinatorial definition of a supersymmetric S-function to a Weyl type formula was proved by Pragacz [1]. In the present paper we show how this identity gives rise to a new algorithm for Littlewood-Richardson coefficients, which is easy to implement. We discuss the present algorithm, its implementation, and some applications.

The exponential cosine screened Coulomb potential in the framework of algebraic perturbation theory

High accuracy approximations for the bound state energies of the exponential cosine screened Coulomb potential are obtained by means of algebraic perturbation calculations.

Total exchange algorithms on ‘sandwich graphs’

Abstract A ‘sandwich graph’ is obtained by connecting the corresponding vertices of two copies of a given graph. We show how a good total exchange algorithm for a sandwich graph can be obtained from a good total exchange algorithm for its components. Applying this result to the hypercube, we obtain an optimal algorithm for total exchange on the hypercube.