PUBLISHED PAPERS #04.01
| Chinara Gadjieva. Approximate Solution of the Simple Hypersingular Integral Equations with Hilbert Kernel |
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| Abstract. In the present paper, the hypersingular integral operator with Hilbert kernel is approximated by a sequence of operators of the special form, it is proved that, the approximating operators strongly converge to the operator of the special form, for a trigonometric polynomial of degree not higher than and is given a new method for the approximate solution of hypersingular integral equations of the first kind with Hilbert kernel and as an example is shown its application to a certain problem. The proposed method is straightforward to calculate, making the new approximate method reliable and easy to apply and the obtained numerical results demonstrate the stability and efficiency of the approach. |
| Keywords: hypersingular integral operator, Hilbert kernel, hypersingular integral equation, best mean-square approximation, convergence |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.031 |