An Efficient Galerkin BEM to Compute High Acoustic Eigenfrequencies

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Mario Durán ◽  
Jean-Claude Nédélec ◽  
Sebastián Ossandón
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
High Frequency ◽  
High Accuracy ◽  
Integral Representations ◽  
Stability And Convergence ◽  
Symmetric Matrices ◽  
Frequency Interval ◽  
Numerical Treatment ◽  
The Stability

An efficient numerical method, using integral equations, is developed to calculate precisely the acoustic eigenfrequencies and their associated eigenvectors, located in a given high frequency interval. It is currently known that the real symmetric matrices are well adapted to numerical treatment. However, we show that this is not the case when using integral representations to determine with high accuracy the spectrum of elliptic, and other related operators. Functions are evaluated only in the boundary of the domain, so very fine discretizations may be chosen to obtain high eigenfrequencies. We discuss the stability and convergence of the proposed method. Finally we show some examples.

scholarly journals Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

2019 ◽  
Vol 4 (2) ◽  
pp. 395-406 ◽  
Author(s):  
R. A. Mundewadi ◽  
Kumbinarasaiah S
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Integral Equations ◽  
High Accuracy ◽  
Algebraic Equations ◽  
Wavelet Method

AbstractA numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

scholarly journals Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Habtamu Garoma Debela ◽  
Solomon Bati Kejela ◽  
Ayana Deressa Negassa
Keyword(s):  
Numerical Method ◽  
Difference Equations ◽  
Oscillatory Behavior ◽  
Singularly Perturbed ◽  
Stability And Convergence ◽  
Uniform Mesh ◽  
Small Shift ◽  
Exponentially Fitted ◽  
Maximum Absolute Errors ◽  
The Stability

This paper presents a numerical method to solve singularly perturbed differential-difference equations. The solution of this problem exhibits layer or oscillatory behavior depending on the sign of the sum of the coefficients in reaction terms. A fourth-order exponentially fitted numerical scheme on uniform mesh is developed. The stability and convergence of the proposed method have been established. The effect of delay parameter (small shift) on the boundary layer(s) has also been analyzed and depicted in graphs. The applicability of the proposed scheme is validated by implementing it on four model examples. Maximum absolute errors in comparison with the other numerical experiments are tabulated to illustrate the proposed method.

scholarly journals Stability and Convergence of Solutions to Volterra Integral Equations on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Eleonora Messina ◽  
Antonia Vecchio
Keyword(s):  
Integral Equations ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Volterra Integral Equations ◽  
Stability And Convergence ◽  
Time Behavior ◽  
Convergence Properties ◽  
Convergence Of Solutions ◽  
Long Time ◽  
The Stability

We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity.

scholarly journals A numerical method using Laplace-like transform and variational theory for solving time-fractional nonlinear partial differential equations with proportional delay

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Alemu Senbeta Bekela ◽  
Melisew Tefera Belachew ◽  
Getinet Alemayehu Wole
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Nonlinear Partial Differential Equations ◽  
Stability And Convergence ◽  
Test Problems ◽  
Proportional Delay ◽  
Variational Theory ◽  
Partial Differential ◽  
The Stability

Abstract Time-fractional nonlinear partial differential equations (TFNPDEs) with proportional delay are commonly used for modeling real-world phenomena like earthquake, volcanic eruption, and brain tumor dynamics. These problems are quite challenging, and the transcendental nature of the delay makes them even more difficult. Hence, the development of efficient numerical methods is open for research. In this paper, we use the concepts of Laplace-like transform and variational theory to develop a new numerical method for solving TFNPDEs with proportional delay. The stability and convergence of the method are analyzed in the Banach sense. The efficiency of the proposed method is demonstrated by solving some test problems. The numerical results show that the proposed method performs much better than some recently developed methods and enables us to obtain more accurate solutions.

scholarly journals Numerical treatment of singularly perturbed delay reaction-diffusion equations

2020 ◽  
Vol 12 (1) ◽  
pp. 15-24
Author(s):  
Gashu Gadisa Kiltu ◽  
Gemechis File Duressa ◽  
Tesfaye Aga Bullo
Keyword(s):  
Time Delay ◽  
Present Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Stability And Convergence ◽  
Numerical Treatment ◽  
The Stability

This paper presents a uniform convergent numerical method for solving singularly perturbed delay reaction-diffusion equations. The stability and convergence analysis are investigated. Numerical results are tabulated and the effect of the layer on the solution is examined. In a nutshell, the present method improves the findings of some existing numerical methods reported in the literature. Keywords: Singularly perturbed, Time delay, Reaction-diffusion equation, Layer

scholarly journals Numerical treatment of the generalized Love integral equation

2020 ◽  
Author(s):  
Luisa Fermo ◽  
Maria Grazia Russo ◽  
Giada Serafini
Keyword(s):  
Integral Equation ◽  
Quadrature Formula ◽  
Numerical Procedure ◽  
Quadrature Rule ◽  
Weighted Spaces ◽  
Stability And Convergence ◽  
Numerical Treatment ◽  
Nyström Method ◽  
Numerical Tests ◽  
The Stability

Abstract In this paper, the generalized Love integral equation has been considered. In order to approximate the solution, a Nyström method based on a mixed quadrature rule has been proposed. Such a rule is a combination of a product and a “dilation” quadrature formula. The stability and convergence of the described numerical procedure have been discussed in suitable weighted spaces and the efficiency of the method is shown by some numerical tests.

scholarly journals Method of achievement the high accuracy of the shape of reflectors of mirror antennas of spacecraft

2019 ◽  
Vol 3 (4) ◽  
pp. 200-208
Author(s):  
V. B. Taygin ◽  
А. V. Lopatin
Keyword(s):  
High Frequency ◽  
High Accuracy ◽  
Frequency Interval ◽  
Innovative Design ◽  
Space Antennas ◽  
Different Types ◽  
Radio Signals ◽  
Low Mass ◽  
Mirror Antenna ◽  
New Space

Analysis of conditions, which are required for mirror antennas of spacecrafts destined for transmission of high-frequent radio signals, is done in this paper. These conditions are regarded to resistance and rigidity of the construction features of the material of an antenna’s reflector and its surface’s quality. It is mentioned that the requirements to the accuracy of the reflector’s shape grow together with the frequency of a radio signal. Altogether, the existing constructions of antennas and the producing technologies are not capable to obtain those requirements. The innovative method of controlling the shape of a reflector of a mirror antenna is presented in the paper. Its application gives an opportunity to produce constructions with a highly accurate surface. This method deals with the fact that the required accuracy of a reflector can be achieved via elastic deformation of its shell. Design of the regulating units for different types of reflectors is developed. We propose an algorithm of choosing the number of the regulating units and their locations. This algorithm uses the results of finite-element modal analysis of a reflector’s shell. Innovative design of axisymmetric and offset reflectors which shell’s shape can arise from controlled deformation is developed. We also suggest the design of the reflector’s shell with a timber with regulating units on it. Such design provides an opportunity to significantly decrease the number of the regulating units. Project of the reflector with a timber and console rods possessing low mass and high stiffness is developed. Method of achievement the high accuracy of a reflector, presented in the paper, can be applied to design of new space antennas operating in high-frequency interval.

scholarly journals Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

2019 ◽  
Vol 4 (1) ◽  
pp. 169-180 ◽  
Author(s):  
R. A. Mundewadi ◽  
S. Kumbinarasaiah
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Integral Equations ◽  
High Accuracy ◽  
Algebraic Equations ◽  
Wavelet Method

AbstractA numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

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