Approximate solution of singular integral equations of the first kind with Cauchy kernel
In this work a study of efficient approximate methods for solving the Cauchy type singular integral equations (CSIEs) of the first kind, over a finite interval, is presented. In the solution, Chebyshev polynomials of the first kind, Tn(x)Tn(x), second kind, Un(x)Un(x), third kind, Vn(x)Vn(x), and fo...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2009
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/13254/1/Approximate%20solution%20of%20singular%20integral%20equations%20of%20the%20first%20kind%20with%20Cauchy%20kernel.pdf |
| _version_ | 1825945201186701312 |
|---|---|
| author | Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri Mahiub, Mohammad Abdulkawi |
| author_facet | Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri Mahiub, Mohammad Abdulkawi |
| author_sort | Eshkuratov, Zainidin K. |
| collection | UPM |
| description | In this work a study of efficient approximate methods for solving the Cauchy type singular integral equations (CSIEs) of the first kind, over a finite interval, is presented. In the solution, Chebyshev polynomials of the first kind, Tn(x)Tn(x), second kind, Un(x)Un(x), third kind, Vn(x)Vn(x), and fourth kind, Wn(x)Wn(x), corresponding to respective weight functions View the MathML sourceW(1)(x)=(1−x2)−12, View the MathML sourceW(2)(x)=(1−x2)12,W(3)(x)=(1+x)12(1−x)−12 and View the MathML sourceW(4)(x)=(1+x)−12(1−x)12, have been used to obtain systems of linear algebraic equations. These systems are solved numerically. It is shown that for a linear force function the method of approximate solution gives an exact solution, and it cannot be generalized to any polynomial of degree nn. Numerical results for other force functions are given to illustrate the efficiency and accuracy of the method. |
| first_indexed | 2024-03-06T07:27:48Z |
| format | Article |
| id | upm.eprints-13254 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:27:48Z |
| publishDate | 2009 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | upm.eprints-132542019-10-31T04:06:57Z http://psasir.upm.edu.my/id/eprint/13254/ Approximate solution of singular integral equations of the first kind with Cauchy kernel Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri Mahiub, Mohammad Abdulkawi In this work a study of efficient approximate methods for solving the Cauchy type singular integral equations (CSIEs) of the first kind, over a finite interval, is presented. In the solution, Chebyshev polynomials of the first kind, Tn(x)Tn(x), second kind, Un(x)Un(x), third kind, Vn(x)Vn(x), and fourth kind, Wn(x)Wn(x), corresponding to respective weight functions View the MathML sourceW(1)(x)=(1−x2)−12, View the MathML sourceW(2)(x)=(1−x2)12,W(3)(x)=(1+x)12(1−x)−12 and View the MathML sourceW(4)(x)=(1+x)−12(1−x)12, have been used to obtain systems of linear algebraic equations. These systems are solved numerically. It is shown that for a linear force function the method of approximate solution gives an exact solution, and it cannot be generalized to any polynomial of degree nn. Numerical results for other force functions are given to illustrate the efficiency and accuracy of the method. Elsevier 2009-05 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/13254/1/Approximate%20solution%20of%20singular%20integral%20equations%20of%20the%20first%20kind%20with%20Cauchy%20kernel.pdf Eshkuratov, Zainidin K. and Nik Long, Nik Mohd Asri and Mahiub, Mohammad Abdulkawi (2009) Approximate solution of singular integral equations of the first kind with Cauchy kernel. Applied Mathematics Letters, 22 (5 ). pp. 651-657. ISSN 0893-9659; ESSN: 1873-5452 https://www.sciencedirect.com/science/article/pii/S0893965908002577?via%3Dihub#! 10.1016/j.aml.2008.08.001 |
| spellingShingle | Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri Mahiub, Mohammad Abdulkawi Approximate solution of singular integral equations of the first kind with Cauchy kernel |
| title | Approximate solution of singular integral equations of the first kind with Cauchy kernel |
| title_full | Approximate solution of singular integral equations of the first kind with Cauchy kernel |
| title_fullStr | Approximate solution of singular integral equations of the first kind with Cauchy kernel |
| title_full_unstemmed | Approximate solution of singular integral equations of the first kind with Cauchy kernel |
| title_short | Approximate solution of singular integral equations of the first kind with Cauchy kernel |
| title_sort | approximate solution of singular integral equations of the first kind with cauchy kernel |
| url | http://psasir.upm.edu.my/id/eprint/13254/1/Approximate%20solution%20of%20singular%20integral%20equations%20of%20the%20first%20kind%20with%20Cauchy%20kernel.pdf |
| work_keys_str_mv | AT eshkuratovzainidink approximatesolutionofsingularintegralequationsofthefirstkindwithcauchykernel AT niklongnikmohdasri approximatesolutionofsingularintegralequationsofthefirstkindwithcauchykernel AT mahiubmohammadabdulkawi approximatesolutionofsingularintegralequationsofthefirstkindwithcauchykernel |