Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule
In this paper, the generalized Simpson's rule (GSR) is applied to solve linear Fredholm-Stieltjes integral equations of the second kind (LFSIESK). A numerical example is presented to illustrate the method by using Maple. In some cases depending on the number of subintervals “n” , the results a...
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Kyrgyz Turkish Manas University
2016-05-01
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| Series: | MANAS: Journal of Engineering |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/576716 |
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| author | A. Asanov S. Yanık |
| author_facet | A. Asanov S. Yanık |
| author_sort | A. Asanov |
| collection | DOAJ |
| description | In this paper, the generalized Simpson's rule (GSR) is applied to solve linear Fredholm-Stieltjes integral equations of the second kind (LFSIESK). A numerical example is presented to illustrate the method by using Maple. In some cases depending on the number of subintervals “n” , the results are calculated and compared. The graph of these results is plotted. An algorithm of this application is given by using Maple. The theory of integral equation with its applications plays an important role in applied mathematics. Integral equations are used as mathematical models for many and varied physical situations and they also occur as reformulations of other mathematical problems [7]. For many integral equations, it is necessary to use approximation methods. As an example, most of the geophysical problems connected with electromagnetic and seismic wave propagation can only be solved approximately. Among theintegral equations, linear Fredholm integral equations of second kind is one of the most popular types of integral equations [7] [13]. Many approximation methods can be used to solve linear Fredholm integral equations of second kind. However, only a few of them are useful to solve LFSIESK. The generalized Simpson's rule is one of the most suitable method with its pretty close result to solve LFSIESK. |
| format | Article |
| id | doaj-art-3b9eff86520c4ba8b7885838c8e58909 |
| institution | Kabale University |
| issn | 1694-7398 |
| language | English |
| publishDate | 2016-05-01 |
| publisher | Kyrgyz Turkish Manas University |
| record_format | Article |
| series | MANAS: Journal of Engineering |
| spelling | doaj-art-3b9eff86520c4ba8b7885838c8e589092025-02-03T12:02:31ZengKyrgyz Turkish Manas UniversityMANAS: Journal of Engineering1694-73982016-05-01411111437Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s ruleA. Asanov0S. Yanık1Kırgızistan Türkiye Manas Üniversitesi, Bişkek, KırgızistanKırgızistan Türkiye Manas Üniversitesi, Bişkek, KırgızistanIn this paper, the generalized Simpson's rule (GSR) is applied to solve linear Fredholm-Stieltjes integral equations of the second kind (LFSIESK). A numerical example is presented to illustrate the method by using Maple. In some cases depending on the number of subintervals “n” , the results are calculated and compared. The graph of these results is plotted. An algorithm of this application is given by using Maple. The theory of integral equation with its applications plays an important role in applied mathematics. Integral equations are used as mathematical models for many and varied physical situations and they also occur as reformulations of other mathematical problems [7]. For many integral equations, it is necessary to use approximation methods. As an example, most of the geophysical problems connected with electromagnetic and seismic wave propagation can only be solved approximately. Among theintegral equations, linear Fredholm integral equations of second kind is one of the most popular types of integral equations [7] [13]. Many approximation methods can be used to solve linear Fredholm integral equations of second kind. However, only a few of them are useful to solve LFSIESK. The generalized Simpson's rule is one of the most suitable method with its pretty close result to solve LFSIESK.https://dergipark.org.tr/en/download/article-file/576716yaklaşık çözümlerlineer fredholm-stieltjes i̇ntegral denklemlerisimpson kuralı.approximate solutionslinear fredholm-stieltjes integral equationssimpson's rule. |
| spellingShingle | A. Asanov S. Yanık Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule MANAS: Journal of Engineering yaklaşık çözümler lineer fredholm-stieltjes i̇ntegral denklemleri simpson kuralı. approximate solutions linear fredholm-stieltjes integral equations simpson's rule. |
| title | Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule |
| title_full | Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule |
| title_fullStr | Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule |
| title_full_unstemmed | Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule |
| title_short | Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule |
| title_sort | solving linear fredholm stieltjes integral equations of the second kind by using the generalized simpson s rule |
| topic | yaklaşık çözümler lineer fredholm-stieltjes i̇ntegral denklemleri simpson kuralı. approximate solutions linear fredholm-stieltjes integral equations simpson's rule. |
| url | https://dergipark.org.tr/en/download/article-file/576716 |
| work_keys_str_mv | AT aasanov solvinglinearfredholmstieltjesintegralequationsofthesecondkindbyusingthegeneralizedsimpsonsrule AT syanık solvinglinearfredholmstieltjesintegralequationsofthesecondkindbyusingthegeneralizedsimpsonsrule |