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## A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials

#### Behrouz PARSA MOGHADDAM [1] , J. A. TENREİRO MACHADO [2] , Parisa SATTARİ SHAJARİ [3] , Zeynab SALAMAT MOSTAGHİM [4]

A numerical algorithm based on Hermite polynomials for solving the Cauchy singular integral equation in the general form is presented. The Hermite polynomial interpolation of unknown functions is first introduced. The proposed technique is then used for approximating the solution of the Cauchy singular integral equation. This approach requires the solution of a system of linear algebraic equations. Two examples demonstrate the effectiveness of the proposed method.
Cauchy singular integral equation, Hermite polynomials, Numerical schemes, Interpolation theory
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Primary Language en Mathematics Mathematics Orcid: 0000-0003-4957-9028Author: Behrouz PARSA MOGHADDAM (Primary Author)Institution: University of LahijanCountry: Iran Orcid: 0000-0003-4274-4879Author: J. A. TENREİRO MACHADO Institution: Institute of Engineering, PortoCountry: Portugal Orcid: 0000-0001-6014-4864Author: Parisa SATTARİ SHAJARİ Institution: University of LahijanCountry: Iran Orcid: 0000-0003-2352-976XAuthor: Zeynab SALAMAT MOSTAGHİM Institution: University of LahijanCountry: Iran Publication Date : June 2, 2020
 Bibtex @research article { hujms474938, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {974 - 983}, doi = {10.15672/hujms.474938}, title = {A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials}, key = {cite}, author = {Parsa Moghaddam, Behrouz and Tenrei̇ro Machado, J. A. and Sattari̇ Shajari̇, Parisa and Salamat Mostaghi̇m, Zeynab} } APA Parsa Moghaddam, B , Tenrei̇ro Machado, J , Sattari̇ Shajari̇, P , Salamat Mostaghi̇m, Z . (2020). A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials . Hacettepe Journal of Mathematics and Statistics , 49 (3) , 974-983 . DOI: 10.15672/hujms.474938 MLA Parsa Moghaddam, B , Tenrei̇ro Machado, J , Sattari̇ Shajari̇, P , Salamat Mostaghi̇m, Z . "A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 974-983 Chicago Parsa Moghaddam, B , Tenrei̇ro Machado, J , Sattari̇ Shajari̇, P , Salamat Mostaghi̇m, Z . "A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 974-983 RIS TY - JOUR T1 - A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials AU - Behrouz Parsa Moghaddam , J. A. Tenrei̇ro Machado , Parisa Sattari̇ Shajari̇ , Zeynab Salamat Mostaghi̇m Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.474938 DO - 10.15672/hujms.474938 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 974 EP - 983 VL - 49 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.474938 UR - https://doi.org/10.15672/hujms.474938 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials %A Behrouz Parsa Moghaddam , J. A. Tenrei̇ro Machado , Parisa Sattari̇ Shajari̇ , Zeynab Salamat Mostaghi̇m %T A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 3 %R doi: 10.15672/hujms.474938 %U 10.15672/hujms.474938 ISNAD Parsa Moghaddam, Behrouz , Tenrei̇ro Machado, J. A. , Sattari̇ Shajari̇, Parisa , Salamat Mostaghi̇m, Zeynab . "A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials". Hacettepe Journal of Mathematics and Statistics 49 / 3 (June 2020): 974-983 . https://doi.org/10.15672/hujms.474938 AMA Parsa Moghaddam B , Tenrei̇ro Machado J , Sattari̇ Shajari̇ P , Salamat Mostaghi̇m Z . A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 974-983. Vancouver Parsa Moghaddam B , Tenrei̇ro Machado J , Sattari̇ Shajari̇ P , Salamat Mostaghi̇m Z . A numerical algorithm for solving the Cauchy singular integral equation based on Hermite polynomials. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 974-983.

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