The Numerical Treatment of Integral Equations.

1979 ◽  
Vol 33 (147) ◽  
pp. 1123
Author(s):  
Kendall Atkinson ◽  
Christopher T. H. Baker
Keyword(s):  
Integral Equations ◽  
Numerical Treatment

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.

The Numerical Treatment of Integral Equations (C. T. H. Baker)

SIAM Review ◽  
1981 ◽  
Vol 23 (2) ◽  
pp. 266-267 ◽  
Author(s):  
P. M. Prenter
Keyword(s):  
Integral Equations ◽  
Numerical Treatment

Numerical treatment of integral equations on iPSC

1993 ◽  
Vol 12 (5) ◽  
pp. 473-483
Author(s):  
Armel de La Bourdonnaye
Keyword(s):  
Integral Equations ◽  
Numerical Treatment

Numerical Treatment of Nonlinear Stochastic Itô–Volterra Integral Equations by Piecewise Spectral-Collocation Method

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Fakhrodin Mohammadi
Keyword(s):  
Approximate Solution ◽  
Finite Number ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Lagrange Interpolation ◽  
Interpolation Method ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Treatment ◽  
Nonlinear Integral Equations

This paper deals with the approximate solution of nonlinear stochastic Itô–Volterra integral equations (NSIVIE). First, the solution domain of these nonlinear integral equations is divided into a finite number of subintervals. Then, the Chebyshev–Gauss–Radau points along with the Lagrange interpolation method are employed to get approximate solution of NSIVIE in each subinterval. The method enjoys the advantage of providing the approximate solutions in the entire domain accurately. The convergence analysis of the numerical method is also provided. Some illustrative examples are given to elucidate the efficiency and applicability of the proposed method.

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