A finite B-spline basis set for accurate diatomic molecule calculations

2003 ◽  
Vol 25 (3) ◽  
pp. 368-374 ◽  
Author(s):  
A. N. Artemyev ◽  
E. V. Ludeña ◽  
V. V. Karasiev ◽  
A. J. Hernández
Keyword(s):  
Diatomic Molecule ◽  
Basis Set ◽  
B Spline ◽  
Spline Basis

scholarly journals Application of the Hylleraas- B -spline basis set: Nonrelativistic Bethe logarithm of helium

2019 ◽  
Vol 100 (4) ◽  
Author(s):  
San-Jiang Yang ◽  
Yong-Bo Tang ◽  
Yong-Hua Zhao ◽  
Ting-Yun Shi ◽  
Hao-Xue Qiao
Keyword(s):  
Basis Set ◽  
B Spline ◽  
Spline Basis

ELECTRONIC STRUCTURE CALCULATIONS OF LOW-DIMENSIONAL SEMICONDUCTOR STRUCTURES USING B-SPLINE BASIS FUNCTIONS

2005 ◽  
Vol 16 (02) ◽  
pp. 237-251
Author(s):  
BORA DIKMEN ◽  
MEHMET TOMAK
Keyword(s):  
Electronic Structure Calculations ◽  
Basis Functions ◽  
Basis Set ◽  
B Spline ◽  
B Splines ◽  
Semiconductor Structures ◽  
Spline Basis ◽  
The Finite Difference Method ◽  
Low Dimensional ◽  
Structure Calculations

An efficient method for the low-dimensional semiconductor structure is investigated. The method is applied to symmetric double rectangular quantum well as an example. A basis set of Cubic B-Splines is used as localized basis functions. The method compares well with analytical solutions and the finite difference method.

scholarly journals Application of the Hylleraas- B -spline basis set: Static dipole polarizabilities of helium

2017 ◽  
Vol 95 (6) ◽  
Author(s):  
San-Jiang Yang ◽  
Xue-Song Mei ◽  
Ting-Yun Shi ◽  
Hao-Xue Qiao
Keyword(s):  
Basis Set ◽  
B Spline ◽  
Spline Basis ◽  
Dipole Polarizabilities

scholarly journals Application of B-splines in determining the eigenspectrum of diatomic molecules: robust numerical description of halo-state and Feshbach molecules

2009 ◽  
Vol 87 (1) ◽  
pp. 67-74 ◽  
Author(s):  
A Derevianko ◽  
E Luc-Koenig ◽  
F Masnou-Seeuws
Keyword(s):  
Diatomic Molecules ◽  
Scattering Length ◽  
Bound State ◽  
Basis Set ◽  
Dissociation Limit ◽  
Universal Relation ◽  
B Spline ◽  
B Splines ◽  
Feshbach Molecules ◽  
Spline Basis

The B-spline basis-set method is applied to determining the rovibrational eigenspectrum of diatomic molecules. Particular attention is paid to a challenging numerical task of an accurate and efficient description of the vibrational levels near the dissociation limit (halo-state and Feshbach molecules). Advantages of using B-splines are highlighted by comparing the performance of the method with that of the commonly used discrete-variable representation (DVR) approach. Several model cases, including the Morse potential and realistic potentials with 1/R3 and 1/R6 long-range dependence of the internuclear separation are studied. We find that the B-spline method is superior to the DVR approach and it is robust enough to properly describe the Feshbach molecules. The developed numerical method is applied to studying the universal relation of the energy of the last bound state to the scattering length. We illustrate numerically the validity of the quantum-defect-theoretic formulation of such a relation for a 1/R6 potential.PACS Nos.: 31.15.–p,34.50.Cx

Solution of non-linear time fractional telegraph equation with source term using B-spline and Caputo derivative

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdul Majeed ◽  
Mohsin Kamran ◽  
Noreen Asghar
Keyword(s):  
Caputo Derivative ◽  
Numerical Solutions ◽  
Linear Time ◽  
Initial Boundary ◽  
Telegraph Equation ◽  
Test Problems ◽  
Von Neumann ◽  
B Spline ◽  
Nonlinear Part ◽  
Spline Basis

Abstract This article focusses on the implementation of cubic B-spline approach to investigate numerical solutions of inhomogeneous time fractional nonlinear telegraph equation using Caputo derivative. L1 formula is used to discretize the Caputo derivative, while B-spline basis functions are used to interpolate the spatial derivative. For nonlinear part, the existing linearization formula is applied after generalizing it for all positive integers. The algorithm for the simulation is also presented. The efficiency of the proposed scheme is examined on three test problems with different initial boundary conditions. The influence of parameter α on the solution profile for different values is demonstrated graphically and numerically. Moreover, the convergence of the proposed scheme is analyzed and the scheme is proved to be unconditionally stable by von Neumann Fourier formula. To quantify the accuracy of the proposed scheme, error norms are computed and was found to be effective and efficient for nonlinear fractional partial differential equations (FPDEs).

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

1990 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
The Finite Element Method ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Spline Basis ◽  
Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

scholarly journals Quasi Cubic Trigonometric Curve and Surface

2019 ◽  
Author(s):  
Guicang Zhang ◽  
Kai Wang
Keyword(s):  
Partition Of Unity ◽  
Shape Features ◽  
Bernstein Basis ◽  
Order Continuity ◽  
B Spline ◽  
Spline Curve ◽  
Totally Positive ◽  
Chebyshev Space ◽  
Spline Basis ◽  
Cutting Algorithm

Firstly, a new set of Quasi-Cubic Trigonometric Bernstein basis with two tension shape parameters is constructed, and we prove that it is an optimal normalized totally basis in the framework of Quasi Extended Chebyshev space. And the Quasi-Cubic Trigonometric Bézier curve is generated by the basis function and the cutting algorithm of the curve are given, the shape features (cusp, inflection point, loop and convexity) of the Quasi-Cubic Trigonometric Bézier curve are analyzed by using envelope theory and topological mapping; Next we construct the non-uniform Quasi-Cubic Trigonometric B-spline basis by assuming the linear combination of the optimal normalized totally positive basis have partition of unity and continuity, and its expression is obtained. And the non-uniform B-spline basis is proved to have totally positive and high-order continuity. Finally, the non-uniform Quasi Cubic Trigonometric B-spline curve and surface are defined, the shape features of the non-uniform Quasi-Cubic Trigonometric B-spline curve are discussed, and the curve and surface are proved to be continuous.

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