Galerkin methods for eigenvalue problem of an integral operator with logarithmic kernel

2017 ◽  
Vol 25 (2) ◽  
pp. 235-251 ◽  
Author(s):  
Bijaya Laxmi Panigrahi
Keyword(s):  
Integral Operator ◽  
Eigenvalue Problem ◽  
Galerkin Methods ◽  
Logarithmic Kernel

scholarly journals Acceleration of Weak Galerkin Methods for the Laplacian Eigenvalue Problem

2018 ◽  
Vol 79 (2) ◽  
pp. 914-934
Author(s):  
Qilong Zhai ◽  
Hehu Xie ◽  
Ran Zhang ◽  
Zhimin Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Galerkin Methods ◽  
Weak Galerkin ◽  
Laplacian Eigenvalue

APPLICATION OF CLENSHAW–CURTIS METHOD IN CONFINED TIME OF ARRIVAL OPERATOR EIGENVALUE PROBLEM

2008 ◽  
Vol 19 (05) ◽  
pp. 821-844 ◽  
Author(s):  
ROBERTO S. VITANCOL ◽  
ERIC A. GALAPON
Keyword(s):  
Integral Operator ◽  
Eigenvalue Problem ◽  
Harmonic Oscillator ◽  
Analytic Solutions ◽  
Time Of Arrival ◽  
Eigenvalues And Eigenfunctions ◽  
Nyström Method ◽  
Nystrom Method

The Clenshaw–Curtis method in discretizing a Fredholm integral operator is applied to solving the confined time of arrival operator eigenvalue problem. The accuracy of the method is measured against the known analytic solutions for the noninteracting case, and its performance compared against the well-known Nystrom method. It is found that Clenshaw–Curtis's is superior to Nystrom's. In particular, Nystrom method yields at most five correct decimal places for the eigenvalues and eigenfunctions, while Clenshaw–Curtis yields eigenvalues correct to 16 decimal places and eigenfunctions up to 15 decimal places for the same number of quadrature points. Moreover, Clenshaw–Curtis's accuracy in the eigenvalues is uniform over a determinable range of the computed eigenvalues for a given number of quadrature abscissas. Clenshaw–Curtis is then applied to the harmonic oscillator confined time of arrival operator eigenvalue problem.

Sign in / Sign up

Export Citation Format

Share Document