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.

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 A discrete method for the logarithmic-kernel integral equation on an open arc

1993 ◽  
Vol 34 (4) ◽  
pp. 401-418 ◽  
Author(s):  
S. Prössdorf ◽  
J. Saranen ◽  
I. H. Sloan
Keyword(s):  
Integral Equation ◽  
Stability And Convergence ◽  
Quadrature Method ◽  
Closed Curves ◽  
Discrete Method ◽  
Logarithmic Kernel ◽  
Quadrature Scheme ◽  
The Family ◽  
The Stability ◽  
Symm’S Integral Equation

AbstractHere we discuss the stability and convergence of a quadrature method for Symm's integral equation on an open smooth arc. The method is an adaptation of an approach considered by Sloan and Burn for closed curves. Before applying the quadrature scheme, we use a cosine substitution to remove the endpoint singularity of the solution. The family of methods includes schemes with any order O(hp) of convergence.

scholarly journals Novel Second-Order Accurate Implicit Numerical Methods for the Riesz Space Distributed-Order Advection-Dispersion Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
X. Wang ◽  
F. Liu ◽  
X. Chen
Keyword(s):  
Numerical Methods ◽  
Quadrature Rule ◽  
Second Order ◽  
Riesz Space ◽  
Stability And Convergence ◽  
Dispersion Equations ◽  
Advection Dispersion ◽  
Alternating Direction ◽  
The Stability ◽  
Distributed Order

We derive and analyze second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations (RSDO-ADE) in one-dimensional (1D) and two-dimensional (2D) cases, respectively. Firstly, we discretize the Riesz space distributed-order advection-dispersion equations into multiterm Riesz space fractional advection-dispersion equations (MT-RSDO-ADE) by using the midpoint quadrature rule. Secondly, we propose a second-order accurate implicit numerical method for the MT-RSDO-ADE. Thirdly, stability and convergence are discussed. We investigate the numerical solution and analysis of the RSDO-ADE in 1D case. Then we discuss the RSDO-ADE in 2D case. For 2D case, we propose a new second-order accurate implicit alternating direction method, and the stability and convergence of this method are proved. Finally, numerical results are presented to support our theoretical analysis.

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 Error bounds for a Gauss-type quadrature rule to evaluate hypersingular integrals

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2525-2543
Author(s):  
Bonis de ◽  
Donatella Occorsio
Keyword(s):  
Quadrature Rule ◽  
Density Functions ◽  
Finite Part ◽  
Type Condition ◽  
Hypersingular Integrals ◽  
Numerical Tests ◽  
Hadamard Finite Part ◽  
Gauss Type ◽  
Computational Aspects ◽  
The Stability

In the present paper we consider hypersingular integrals of the following type =?+?,0 f(x)/(x-t)p+1 w?(x)dx, where the integral is understood in the Hadamard finite part sense, p is a positive integer, w?(x) = e-xx? is a Laguerre weight of parameter ? ? 0 and t > 0. In [6] we proposed an efficient numerical algorithm for approximating (1), focusing our attention on the computational aspects and on the efficient implementation of the method. Here, we introduce the method discussing the theoretical aspects, by proving the stability and the convergence of the procedure for density functions f s.t. f(p) satisfies a Dini-type condition. For the sake of completeness, we present some numerical tests which support the theoretical estimates.

scholarly journals Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Haiyan Yuan ◽  
Cheng Song
Keyword(s):  
Differential Equations ◽  
Quadrature Formula ◽  
Nonlinear Stability ◽  
Stability And Convergence ◽  
Asymptotically Stable ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Stage Order ◽  
Runge Kutta ◽  
The Stability

This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of(k,l)-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a(k,l)-algebraically stable two-step Runge-Kutta method with0<k<1is proved. For the convergence, the concepts ofD-convergence, diagonally stable, and generalized stage order are firstly introduced; then it is proved by some theorems that if a two-step Runge-Kutta method is algebraically stable and diagonally stable and its generalized stage order isp, then the method with compound quadrature formula isD-convergent of order at leastmin{p,ν}, whereνdepends on the compound quadrature formula.

scholarly journals Numerical simulation of periodic MHD casson nanofluid flow through porous stretching sheet

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Abdullah Al-Mamun ◽  
S. M. Arifuzzaman ◽  
Sk. Reza-E-Rabbi ◽  
Umme Sara Alam ◽  
Saiful Islam ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Lewis Number ◽  
Stability And Convergence ◽  
Radiation Absorption ◽  
Physical Parameters ◽  
Theoretical Idea ◽  
Prostate Cancer Therapy ◽  
Flow Through ◽  
Explicit Finite Difference ◽  
The Stability

AbstractThe perspective of this paper is to characterize a Casson type of Non-Newtonian fluid flow through heat as well as mass conduction towards a stretching surface with thermophoresis and radiation absorption impacts in association with periodic hydromagnetic effect. Here heat absorption is also integrated with the heat absorbing parameter. A time dependent fundamental set of equations, i.e. momentum, energy and concentration have been established to discuss the fluid flow system. Explicit finite difference technique is occupied here by executing a procedure in Compaq Visual Fortran 6.6a to elucidate the mathematical model of liquid flow. The stability and convergence inspection has been accomplished. It has observed that the present work converged at, Pr ≥ 0.447 indicates the value of Prandtl number and Le ≥ 0.163 indicates the value of Lewis number. Impact of useful physical parameters has been illustrated graphically on various flow fields. It has inspected that the periodic magnetic field has helped to increase the interaction of the nanoparticles in the velocity field significantly. The field has been depicted in a vibrating form which is also done newly in this work. Subsequently, the Lorentz force has also represented a great impact in the updated visualization (streamlines and isotherms) of the flow field. The respective fields appeared with more wave for the larger values of magnetic parameter. These results help to visualize a theoretical idea of the effect of modern electromagnetic induction use in industry instead of traditional energy sources. Moreover, it has a great application in lung and prostate cancer therapy.

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