Related papers: Improvement of the Basis for the Solution of the D…
A new approach to finite basis sets for the Dirac equation is developed. It solves the problem of spurious states and, as a result, improves the convergence properties of basis set calculations. The efficiency of the method is demonstrated…
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic…
The rigorous two-center approach based on the dual-kinetically balanced finite-basis-set expansion is applied to one-electron, heteronuclear diatomic Bi-Au, U-Pb, and Cf-U quasimolecules. The obtained $1\sigma$ ground-state energies are…
A two-dimensional, fully numerical approach to the solution of four-component Dirac-Fock equation using the moderately long Hermitian basis of B-splines is applied to H, H2+ and H2 in a strong magnetic field. The geometric parameters,…
Two numerical methods are used to evaluate the relativistic spectrum of the two-centre Coulomb problem (for the $H_{2}^{+}$ and $Th_{2}^{179+}$ diatomic molecules) in the fixed nuclei approximation by solving the single particle…
The dual-kinetic-balance (DKB) finite basis set method for solving the Dirac equation for hydrogen-like ions [V. M. Shabaev et al., Phys. Rev. Lett. 93, 130405 (2004)] is extended to problems with a non-local spherically-symmetric…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…
The complete system of the B-spline solutions for the Dirac equation with the parity-nonconserving (PNC) weak interaction effective potential is obtained. This system can be used for the accurate evaluation of the radiative corrections to…
This paper presents a new approach and methodology to solve the second order one dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual…
It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so…
This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial…
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac…
In this paper, we provide a procedure to solve the eigen solutions of Dirac equation with complicated potential approximately. At first, we solve the eigen solutions of a linear Dirac equation with complete eigen system, which approximately…
In the paper, we give methods of construction of dual bases for the B-spline basis and truncated power basis. Explicit formulas for the dual B-spline basis are obtained using the Legendre-like orthogonal basis of the polynomial spline space…
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…
The Dirac equation for H$_2^+$ is solved numerically by expansion in a basis set of two-center exponential functions, using different kinetic balance schemes. Very high precision (27-32 digits) is achieved, either with the dual kinetic…
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the…
The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…