Conference Paper
BibTex RIS Cite

İkinci tür lineer Fredholm-Stieltjes integral denklemlerinin genelleştirilmiş Simpson kuralı ile çözümü

Year 2016, Volume: 4 Issue: 1, 1 - 11, 01.05.2016

Abstract

Bu çalışmada, ikinci tür lineer Fredholm-Stieltjes integral denklemlerinin çözümü için genelleştirilmiş Simpson kuralı uygulanmıştır. Metodu göstermek için Maple programı kullanılarak sayısal bir örnek sunulmuştur. "n"nin alt aralıklarına göre bazı durumlarda sonuçlar hesaplanmış ve karşılaştırılmıştır. Bu sonuçların grafiği çizilmiştir.Maple kullanılarak oluşturulmuş bu uygulamanın algoritması verilmiştir.

Bu çalışmada, ikinci tür lineer Fredholm-Stieltjes integral denklemlerinin çözümü için genelleştirilmiş Simpson kuralı uygulanmıştır. Metodu göstermek için Maple programı kullanılarak sayısal bir örnek sunulmuştur. "n"nin alt aralıklarına göre bazı durumlarda sonuçlar hesaplanmış ve karşılaştırılmıştır. Bu sonuçların grafiği çizilmiştir.Maple kullanılarak oluşturulmuş bu uygulamanın algoritması verilmiştir.

References

  • [1] A. Asanov, M. H. Chelik ve M. Sezer, «Approximating the Stieltjes Integral by Using the Generalized Simpson's Rule,» Com. in Diff. and Difference Eq., cilt 1, no. 3, pp. 1-11, 2012.
  • [2] L.M. Delves , J. Walsh, Numerical Solution of Integral Equations, London: Oxford University Press, 1974.
  • [3] P.Cerone , S.S.Dragomir , «Approximation of the Stieltjes Integral and Applications in Numerical Integration,» Application of Mathematics, pp. 37-47, 2006.
  • [4] F. G. Dressel, «A note on Fredholm-Stieltjes Integral Equations,» Bull. Amer. Mat. Soc., cilt 44, no. 6, pp. 434-437, 1938.
  • [5] A. Chakrabarti , S.C. Martha, «Approximate Solutions of Fredholm Integral Equations of The Second Kind,» Applied Mathematics and Computation, no. 211, p. 459–466, 2009.
  • [6] A. T. Lonseth, «Approximate Solutions of Fredholm-Type Integral Equations,» Bull. Amer. Math. Soc., cilt 60, no. 5, pp. 415-430, 1954.
  • [7] K. E. Atkinson, The Numerical Solution Of Integral Equations Of The Second Kind, Cambridge: Cambridge University Press, 1997.

Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule

Year 2016, Volume: 4 Issue: 1, 1 - 11, 01.05.2016

Abstract

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 the
integral 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. 

References

  • [1] A. Asanov, M. H. Chelik ve M. Sezer, «Approximating the Stieltjes Integral by Using the Generalized Simpson's Rule,» Com. in Diff. and Difference Eq., cilt 1, no. 3, pp. 1-11, 2012.
  • [2] L.M. Delves , J. Walsh, Numerical Solution of Integral Equations, London: Oxford University Press, 1974.
  • [3] P.Cerone , S.S.Dragomir , «Approximation of the Stieltjes Integral and Applications in Numerical Integration,» Application of Mathematics, pp. 37-47, 2006.
  • [4] F. G. Dressel, «A note on Fredholm-Stieltjes Integral Equations,» Bull. Amer. Mat. Soc., cilt 44, no. 6, pp. 434-437, 1938.
  • [5] A. Chakrabarti , S.C. Martha, «Approximate Solutions of Fredholm Integral Equations of The Second Kind,» Applied Mathematics and Computation, no. 211, p. 459–466, 2009.
  • [6] A. T. Lonseth, «Approximate Solutions of Fredholm-Type Integral Equations,» Bull. Amer. Math. Soc., cilt 60, no. 5, pp. 415-430, 1954.
  • [7] K. E. Atkinson, The Numerical Solution Of Integral Equations Of The Second Kind, Cambridge: Cambridge University Press, 1997.
There are 7 citations in total.

Details

Primary Language English
Subjects Engineering
Other ID JA37BY62TY
Journal Section Research Article
Authors

S. Yanık This is me

A. Asanov This is me

Publication Date May 1, 2016
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Yanık, S., & Asanov, A. (2016). Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule. MANAS Journal of Engineering, 4(1), 1-11.
AMA Yanık S, Asanov A. Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule. MJEN. May 2016;4(1):1-11.
Chicago Yanık, S., and A. Asanov. “Solving Linear Fredholm-Stieltjes Integral Equations of the Second Kind by Using the Generalized Simpson’s Rule”. MANAS Journal of Engineering 4, no. 1 (May 2016): 1-11.
EndNote Yanık S, Asanov A (May 1, 2016) Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule. MANAS Journal of Engineering 4 1 1–11.
IEEE S. Yanık and A. Asanov, “Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule”, MJEN, vol. 4, no. 1, pp. 1–11, 2016.
ISNAD Yanık, S. - Asanov, A. “Solving Linear Fredholm-Stieltjes Integral Equations of the Second Kind by Using the Generalized Simpson’s Rule”. MANAS Journal of Engineering 4/1 (May 2016), 1-11.
JAMA Yanık S, Asanov A. Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule. MJEN. 2016;4:1–11.
MLA Yanık, S. and A. Asanov. “Solving Linear Fredholm-Stieltjes Integral Equations of the Second Kind by Using the Generalized Simpson’s Rule”. MANAS Journal of Engineering, vol. 4, no. 1, 2016, pp. 1-11.
Vancouver Yanık S, Asanov A. Solving linear Fredholm-Stieltjes integral equations of the second kind by using the generalized Simpson’s rule. MJEN. 2016;4(1):1-11.

Manas Journal of Engineering 

16155