A modified Nyström method for integral equations with Mellin type kernels

The aim of this paper is to propose a new modified Nyström method for the approximation of the solutions of second kind integral equations with fixed singularities of Mellin convolution type. The stability and the convergence are proved in L2 spaces and error estimates in L2 norm are given. Finally,...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-04, Vol.296, p.512-527
Main Authors: De Bonis, M.C., Laurita, C.
Format: Article
Language:English
Subjects:
Approximation
Convergence
Gaussian rule
Integral equations
Integral equations of Mellin type
Kernels
Lagrange interpolation
Mathematical analysis
Mathematical models
Mellin kernel
Norms
Nyström method
Singularities
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Summary:The aim of this paper is to propose a new modified Nyström method for the approximation of the solutions of second kind integral equations with fixed singularities of Mellin convolution type. The stability and the convergence are proved in L2 spaces and error estimates in L2 norm are given. Finally, numerical tests showing the effectiveness of the method are presented.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.10.010