On projection method for numerical solution of hypersingular integral equations of the first kind combined with quadrature methods

The Fredholm integral equations of the first kind with two regular and hypersingular kernels are considered on [−1, 1]. The hypersingular kernel is considered smooth enough with no additional conditions. A projection method based on second kind Chebyshev polynomials approximation, combined with quad...

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Bibliographic Details
Published in:Physica scripta 2023-04, Vol.98 (4), p.45229
Main Authors: Elahi, M R, Mahmoudi, Y, Salimi Shamloo, A, Jahangiri Rad, M
Format: Article
Language:English
Subjects:
Chebyshev polynomials
hypersingular kernel
integral equation
quadrature rules
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Summary:The Fredholm integral equations of the first kind with two regular and hypersingular kernels are considered on [−1, 1]. The hypersingular kernel is considered smooth enough with no additional conditions. A projection method based on second kind Chebyshev polynomials approximation, combined with quadrature integration method, is developed to obtain high accurate approximations. The proposed method reduces the underlying integral equation to a system of algebraic equations. Several illustrative examples are provided to show the efficiency of the method.
ISSN:0031-8949
1402-4896
DOI:10.1088/1402-4896/acc493