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.
[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
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.
[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.
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.