scholarly journals Solving first kind Abel integral equations using the SBA numerical method

2013 ◽  
Vol 1 ◽  
pp. 115-128
Author(s):  
Youssouf Pare ◽  
Abbo Bakari ◽  
Rasmane Yaro ◽  
Blaise Some
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Abel Integral Equations

scholarly journals A family of methods for Abel integral equations of the second kind

1991 ◽  
Vol 34 (2) ◽  
pp. 211-219 ◽  
Author(s):  
H. Brunner ◽  
M.R. Crisci ◽  
E. Russo ◽  
A. Vecchio
Keyword(s):  
Integral Equations ◽  
Abel Integral Equations

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.

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