The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels
A method for approximating the solution of weakly singular Fredholm integral equation of the second kind with highly oscillatory trigonometric kernel is presented. The unknown function is approximated by expansion of Chebychev polynomial and the coefficients are determinated by classical collocation...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/172327 |
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| _version_ | 1832566808033361920 |
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| author | Qinghua Wu |
| author_facet | Qinghua Wu |
| author_sort | Qinghua Wu |
| collection | DOAJ |
| description | A method for approximating the solution of weakly singular Fredholm integral equation of the second kind with highly oscillatory trigonometric kernel is presented. The unknown function is approximated by expansion of Chebychev polynomial and the coefficients are determinated by classical collocation method. Due to the highly oscillatory kernels of integral equation, the discretised collocation equation will give rise to the computation of oscillatory integrals. These integrals are calculated by using recursion formula derived from the fundamental recurrence relation of Chebyshev polynomial. The effectiveness and accuracy of the proposed method are tested by numerical examples. |
| format | Article |
| id | doaj-art-3623462a8a224f36ba057abd6ed36ead |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3623462a8a224f36ba057abd6ed36ead2025-02-03T01:03:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/172327172327The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric KernelsQinghua Wu0School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, ChinaA method for approximating the solution of weakly singular Fredholm integral equation of the second kind with highly oscillatory trigonometric kernel is presented. The unknown function is approximated by expansion of Chebychev polynomial and the coefficients are determinated by classical collocation method. Due to the highly oscillatory kernels of integral equation, the discretised collocation equation will give rise to the computation of oscillatory integrals. These integrals are calculated by using recursion formula derived from the fundamental recurrence relation of Chebyshev polynomial. The effectiveness and accuracy of the proposed method are tested by numerical examples.http://dx.doi.org/10.1155/2014/172327 |
| spellingShingle | Qinghua Wu The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels Journal of Applied Mathematics |
| title | The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels |
| title_full | The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels |
| title_fullStr | The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels |
| title_full_unstemmed | The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels |
| title_short | The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels |
| title_sort | approximate solution of fredholm integral equations with oscillatory trigonometric kernels |
| url | http://dx.doi.org/10.1155/2014/172327 |
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