scholarly journals Numerical Algorithms for Computing Eigenvalues of Discontinuous Dirac System Using Sinc-Gaussian Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. H. Bhrawy ◽  
M. M. Tharwat ◽  
A. Al-Fhaid
Keyword(s):  
Error Analysis ◽  
Numerical Algorithms ◽  
High Accuracy ◽  
Transmission Conditions ◽  
Numerical Results ◽  
New Method ◽  
Dirac System ◽  
Sinc Method ◽  
Dirac Systems ◽  
Gaussian Method

The eigenvalues of a discontinuous regular Dirac systems with transmission conditions at the point of discontinuity are computed using the sinc-Gaussian method. The error analysis of this method for solving discontinuous regular Dirac system is discussed. It shows that the error decays exponentially in terms of the number of involved samples. Therefore, the accuracy of the new method is higher than the classical sinc-method. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented. Comparisons with the classical sinc-method are given.

A NEW INTERFACE CEMENT EQUILIBRATED MORTAR (NICEM) METHOD WITH ROBIN INTERFACE CONDITIONS: THE P1 FINITE ELEMENT CASE

2013 ◽  
Vol 23 (12) ◽  
pp. 2253-2292 ◽  
Author(s):  
CAROLINE JAPHET ◽  
YVON MADAY ◽  
FREDERIC NATAF
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Numerical Results ◽  
New Method ◽  
Interface Conditions ◽  
Well Posed

We design and analyze a new non-conforming domain decomposition method, named the NICEM method, based on Schwarz-type approaches that allows for the use of Robin interface conditions on non-conforming grids. The method is proven to be well posed. The error analysis is performed in 2D and in 3D for P1 elements. Numerical results in 2D illustrate the new method.

Application of Hybrid Subgroup Decomposition Method to Gas Cooled Thermal Reactor Problem

2014 ◽  
Author(s):  
Saam Yasseri ◽  
Farzad Rahnema
Keyword(s):  
Transport Equation ◽  
Computational Efficiency ◽  
Decomposition Method ◽  
High Accuracy ◽  
Numerical Results ◽  
New Method ◽  
Thermal Reactor ◽  
Problem Characteristic ◽  
Group Transport ◽  
Subgroup Decomposition

In this paper, a newly developed hybrid subgroup decomposition method is tested in a 1D problem characteristic of gas cooled thermal reactors (GCR). The new method couples an efficient coarse-group eigenvalue calculation with a set of fine-group transport source iterations to unfold the fine-group flux. It is shown that the new method reproduces the fine-group transport solution by iteratively solving the coarse-group quasi transport equation. The numerical results demonstrate that the new method applied to 1D GCR problem is capable of achieving high accuracy while gaining computational efficiency up to 5 times compared to direct fine-group transport calculations.

scholarly journals Applying Computer Algebra Systems in Approximating the Trigonometric Functions

2018 ◽  
Vol 23 (3) ◽  
pp. 37 ◽  
Author(s):  
Le Quan ◽  
Thái Nhan
Keyword(s):  
Error Analysis ◽  
Computer Algebra ◽  
Numerical Algorithms ◽  
High Accuracy ◽  
Computer Algebra Systems ◽  
Trigonometric Functions ◽  
Modern Computer ◽  
Sine And Cosine Functions ◽  
Cosine Functions ◽  
Very High

We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor’s expansion about a point having a form of kp, k∈Z and p=π/2, and being chosen such that it is closest to the argument. A full error analysis, which takes advantage of current computer algebra systems in approximating π with a very high accuracy, of our proposed methods is provided. A numerical integration application is performed to demonstrate the use of algorithms. Numerical and graphical results are implemented by MAPLE.

scholarly journals A parallel Numerical Algorithm For Solving Some Fractional Integral Equations

2019 ◽  
Vol 32 (1) ◽  
pp. 184
Author(s):  
Khalid Mindeel Mohammed
Keyword(s):  
Neural Network ◽  
Integral Equations ◽  
Numerical Algorithm ◽  
Fractional Integral ◽  
High Accuracy ◽  
Numerical Results ◽  
New Method ◽  
Training Algorithm ◽  
Numerical Examples ◽  
Fractional Equations

In this study, He's parallel numerical algorithm by neural network is applied to type of integration of fractional equations is Abel’s integral equations of the 1st and 2nd kinds. Using a Levenberge – Marquaradt training algorithm as a tool to train the network. To show the efficiency of the method, some type of Abel’s integral equations is solved as numerical examples. Numerical results show that the new method is very efficient problems with high accuracy.

scholarly journals Computation of Spectral Parameter of Discontinuous Dirac Systems with a Gaussian Multiplier

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Mohammed M. Tharwat ◽  
Mohammed A. Alghamdi
Keyword(s):  
Boundary Conditions ◽  
Spectral Parameter ◽  
Worked Examples ◽  
New Technique ◽  
Dirac System ◽  
Sinc Method ◽  
Dirac Systems

We aim in this paper to apply a sinc-Gaussian technique to compute the eigenvalues of a Dirac system which has a discontinuity at one point and contains a spectral parameter in all boundary conditions. We establish the needed properties of eigenvalues of our problem. The error of this method decays exponentially in terms of the number of involved samples. Therefore the accuracy of the new technique is higher than the classical sinc-method. Numerical worked examples with tables and illustrative figures are given at the end of the paper.

scholarly journals Stellar magnetic imaging from spectropolarimetric data

1996 ◽  
Vol 176 ◽  
pp. 53-60 ◽  
Author(s):  
J.-F. Donati
Keyword(s):  
Small Amplitude ◽  
High Accuracy ◽  
Spectral Lines ◽  
New Method ◽  
Doppler Imaging ◽  
Magnetic Imaging ◽  
Active Stars ◽  
Surface Fields ◽  
Very High

In this paper, I will review the capabilities of magnetic imaging (also called Zeeman-Doppler imaging) to reconstruct spot distributions of surface fields from sets of rotationnally modulated Zeeman signatures in circularly polarised spectral lines. I will then outline a new method to measure small amplitude magnetic signals (typically 0.1% for cool active stars) with very high accuracy. Finally, I will present and comment new magnetic images reconstructed from data collected in 1993 December at the Anglo-Australian Telescope (AAT).

A Design of High-Accuracy Displacement Measurement Instrument from Principles of Optics

2012 ◽  
Vol 170-173 ◽  
pp. 2924-2928
Author(s):  
Sheng Biao Chen ◽  
Yun Zhi Tan
Keyword(s):  
Measurement Instrument ◽  
High Accuracy ◽  
Mechanical Tests ◽  
Total Reflection ◽  
Displacement Measurement ◽  
New Method ◽  
Water Volume ◽  
Water Drainage ◽  
Accuracy Of Measurement ◽  
Better Than

In order to measure the water drainage volume in soil mechanical tests accurately, it develop a new method which is based on principles of optics. And from both physical and mathematic aspects, it deduces the mathematic relationship between micro change in displacement and the increment projected on screen. The result shows that total reflection condition is better than refraction condition. What’s more, the screen could show the water volume micro variation clearly, so it can improve the accuracy of measurement.

A new modification of the homotopy perturbation method

2021 ◽  
pp. 095745652199987
Author(s):  
Magaji Yunbunga Adamu ◽  
Peter Ogenyi
Keyword(s):  
Comparative Analysis ◽  
Error Analysis ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Oscillators ◽  
Absolute Error ◽  
New Method ◽  
Optimal Analysis ◽  
Homotopy Perturbation ◽  
Accuracy And Precision

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol’s nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

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