scholarly journals A temporal fourth-order scheme for the first-order acoustic wave equations

2013 ◽  
Vol 194 (3) ◽  
pp. 1473-1485 ◽  
Author(s):  
Guihua Long ◽  
Yubo Zhao ◽  
Jun Zou
Keyword(s):  
Acoustic Wave ◽  
Fourth Order ◽  
Wave Equations ◽  
First Order ◽  
Order Scheme

First-Order Acoustic Wave Equations and Scattering by Atmospheric Turbules.

1997 ◽  
Author(s):  
George H. Goedecke ◽  
Michael DeAntonio ◽  
Harry J. Auvermann
Keyword(s):  
Acoustic Wave ◽  
Wave Equations ◽  
First Order

scholarly journals RECOVERING THE GRADIENTS OF THE SOLUTIONS OF SECOND ORDER HYPERBOLIC EQUATIONS BY INTERPOLATING THE FINITE ELEMENT SOLUTIONS

1995 ◽  
Vol 03 (01) ◽  
pp. 27-56 ◽  
Author(s):  
TAO LIN ◽  
HONG WANG
Keyword(s):  
Finite Element ◽  
Acoustic Wave ◽  
Wave Equations ◽  
Polynomial Interpolation ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Acoustic Wave Equation ◽  
Degree Polynomial ◽  
First Order ◽  
Derivatives Of

We present a technique to generate better approximations to the gradients of the solutions of the second order hyperbolic (acoustic wave) equations by postprocessing finite element solutions with higher degree polynomial interpolation. The postprocessing procedure is inexpensive, local, vectorizable, and parallelizable. In addition, the postprocessing procedure is independent of the computation of the finite element solution; therefore it can be easily incorporated with the existing finite element codes to efficiently generate globally better approximations to the gradients or first order partial derivatives of the main quantities of the acoustic field modeled by the acoustic wave equation.

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

Bhabha first-order wave equations. VI. Exact, closed-form, Foldy-Wouthuysen transformations and solutions

1977 ◽  
Vol 15 (2) ◽  
pp. 433-444 ◽  
Author(s):  
R. A. Krajcik ◽  
Michael Martin Nieto
Keyword(s):  
Closed Form ◽  
Wave Equations ◽  
First Order

The Wave Theory of the Electron

1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Commutative Algebra ◽  
Wave Theory ◽  
Wave Functions ◽  
Linear Differential Equations ◽  
Wave Mechanics ◽  
First Order ◽  
Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

Incommensurately modulated structure of TaGe0.354Te2: application of crenel functions

1996 ◽  
Vol 52 (1) ◽  
pp. 100-109 ◽  
Author(s):  
F. Boucher ◽  
M. Evain ◽  
V. Petříček
Keyword(s):  
Detailed Analysis ◽  
Fourth Order ◽  
X Ray Diffraction ◽  
Third Order ◽  
Modulated Structure ◽  
X Ray ◽  
First Order ◽  
Germanium Telluride ◽  
Orthorhombic Cell ◽  
Orthogonalization Procedure

The incommensurately modulated structure of tantalum germanium telluride, TaGe0.354Te2, was determined by single-crystal X-ray diffraction. The dimensions of the basic orthorhombic cell are a = 6.4394 (5), b = 14.025 (2), c = 3.8456 (5) Å, V = 347.3 (1) Å3 and Z = 4. The (3 + 1)-dimensional superspace group is Pnma(00γ)s00, γ = 0.3544 (3). Refinements on 1641 reflections with I ≥ 3σ(I) converged to R = 0.065 and 0.044 for 526 main reflections and R = 0.061, 0.12, 0.28 and 0.32 for 782 first-order, 237 second-order, 37 third-order and 59 fourth-order satellites, respectively. Since the structure exhibits a strong occupational modulation of both Ta and Ge atoms, along with important displacive modulation waves, crenel functions were used in the refinement in combination with an orthogonalization procedure. Such an approach is shown to be the most convenient and to give reliable coordinations and distances. A detailed analysis of some Te...Te distances is performed, in connection with already known commensurately and incommensurately modulated MAx Te2 structures.

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