Numerical Stability and Convergence of Approximations of Retarded Potential Integral Equations

1994 ◽  
Vol 31 (3) ◽  
pp. 856-875 ◽  
Author(s):  
Penny J. Davies
Keyword(s):  
Integral Equations ◽  
Numerical Stability ◽  
Stability And Convergence ◽  
Numerical Stability And Convergence

NUMERICAL STABILITY AND CONVERGENCE OF APPROXIMATE METHODS FOR CONSERVATION LAWS

1994 ◽  
Vol 05 (02) ◽  
pp. 211-213 ◽  
Author(s):  
V.A. GALKIN
Keyword(s):  
Fluid Dynamics ◽  
Conservation Laws ◽  
Numerical Stability ◽  
Stability And Convergence ◽  
Approximate Methods ◽  
New Approach ◽  
Numerical Stability And Convergence

We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.

Stability of Sequential Modular Time Integration Methods for Coupled Multibody System Models

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Martin Arnold
Keyword(s):  
Differential Equations ◽  
Numerical Stability ◽  
Multibody System ◽  
Time Integration ◽  
Coupled Systems ◽  
Stability And Convergence ◽  
Integration Methods ◽  
System Models ◽  
Time Integration Methods ◽  
Numerical Stability And Convergence

The interacting components of complex technical systems are often described by coupled systems of differential equations. In dynamical simulation, these coupled differential equations have to be solved numerically. Cosimulation techniques, multirate methods, and other approaches that exploit the modular structure of coupled systems are frequently used as alternatives to classical time integration methods. The numerical stability and convergence of such modular time integration methods is studied for a class of sequential modular methods for coupled multibody system models. Theoretical investigations and numerical test results show that the stability of these sequential modular methods may be characterized by a contractivity condition. A linearly implicit stabilization of coupling terms is proposed to guarantee numerical stability and convergence.

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 Solution of second kind Fredholm integral equations by means of Gauss and anti-Gauss quadrature rules

2020 ◽  
Vol 146 (4) ◽  
pp. 699-728
Author(s):  
Patricia Díaz de Alba ◽  
Luisa Fermo ◽  
Giuseppe Rodriguez
Keyword(s):  
Integral Equations ◽  
Numerical Approximation ◽  
Gauss Quadrature ◽  
Upper And Lower Bounds ◽  
Stability And Convergence ◽  
Quadrature Rules ◽  
Fredholm Integral Equations ◽  
Numerical Tests ◽  
Gauss Quadrature Formula ◽  
Gauss Quadrature Rules

AbstractThis paper is concerned with the numerical approximation of Fredholm integral equations of the second kind. A Nyström method based on the anti-Gauss quadrature formula is developed and investigated in terms of stability and convergence in appropriate weighted spaces. The Nyström interpolants corresponding to the Gauss and the anti-Gauss quadrature rules are proved to furnish upper and lower bounds for the solution of the equation, under suitable assumptions which are easily verified for a particular weight function. Hence, an error estimate is available, and the accuracy of the solution can be improved by approximating it by an averaged Nyström interpolant. The effectiveness of the proposed approach is illustrated through different numerical tests.

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