TY - JOUR TT - İkinci tip lineer fredholm integral denklemlerinin chebyshev polinom yaklaşımları AU - Gülsu, Mustafa AU - Öztürk, Yalçın PY - 2010 DA - June JF - Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi PB - Erciyes Üniversitesi WT - DergiPark SN - 1012-2354 SP - 203 EP - 216 VL - 26 IS - 3 KW - Chebyshev polynomials KW - Chebyshev series KW - Chebyshev polynomial solutions KW - Fredholm integral equations KW - approximation method N2 - Bu çalışmada ikinci tip linear Fredholm integral denklemlerinin Chebyshev polinomları ile çözümlerinin bulunması amaçlanmıştır. Bu amaçla yeni Chebyshev matris yöntemi geliştirilmiştir. Belirtilen yöntem denklemdeki bilinmeyen fonksiyonlarının kesilmiş Chebyshev polinomlarının matris formlarının alınması esasına dayanır. Böylece elde edilen denklem sistemi çözülerek Chebyshev polinomlarının katsayıları bulunur. Yöntemin hassasiyeti çeşitli örneklerle açıklanmış ve sonuçlar tartışılmıştır. CR - B. Alpert, G. Beylkin, R. Coifman, V. Rokhlin, Wavelet-like bases for the fast solution of second-kind integral equations, SIAM J. Sci. Comput. 14,159-184,1993. CR - B.C. Choi, S.W. Churchill, A technique for obtaining approximate solutions for a class of integral equations arising in radiative heat transfer, Internat J. Heat Fluid Flow 6 (1),42- 48,1985. CR - L. Reichel, Parallel iterative methods for the solution of Fredholm integral equations of the second kind, in M.T.Heath, Hypercube Multiprocessors, SIAM, Philadelphia, 520- 529,1987. CR - K. Maleknejad, M. Karami, Using the WPG method for solving integral equations of the second kind, Appl. Math. Comput., 166(1),123- 130,2005. CR - E. Babolian, J. Biazar, A.R. Vahidi, The decomposition method applied to systems of Fredholm integral equations of the second kind, Appl. Math. Comput. 148, 443–452,2004. CR - K. Maleknejad, Y. Mahmoudi, Numerical solution of linear Fredholm integral equations by using hybrid Taylor and Block-Pulse functions, Appl. Math. Comput. 149, 799– 806,2004. CR - K. Maleknejad, M. Karami, Numerical solution of non-linear Fredholm integral equations by using multiwavelets in the Petrov–Galerkin method, Appl. Math. Comput.,168(1),102- 110,2005. CR - W. Chen, Z. Lu, An algorithm for Adomian decomposition method, Appl. Math. Comput.159,221–235,2004. CR - Akyüz A., Sezer M., ‘A Chebyshev collocation method for the solution of linear integro- differential equations’,Int.J.Compt.Math.72 (4),491-507,1999. CR - Akyüz, A. and Sezer, M., Chebyshev polynomial solutions of systems of high- orderlinear differential equations with variable coefficients, Appl. Math. Comput.144, 237-247, 2003. CR - Akyüz, A. ‘A Chebyshev polynomial approach for linear Fredholm–Volterra integro- differential equations in the most general form’, Appl. Math. Comput., 181, (1),103-112, 2006. CR - M. Sezer, M. Kaynak, Chebyshev polynomial solutions of linear differential equations, Int. J. Math. Educ. Sci. Technol. 27 (4),607–618,1996. CR - M. Gulsu and M. Sezer, A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Intern. J. Comput. Math. 82 (5),629-642,2005. CR - M. Gulsu and M. Sezer, Polynomial solution of the most general linear Fredholm integrodifferential-difference equations by means of Taylor matrix method, Complex Variables,50(5),367-382,2005. CR - M. Gulsu and M. Sezer, A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Intern. J. Comput. Math. 82 (5),629-642,2005. CR - K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press,Cambridge, 1997. CR - L.M. Delves, J.L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, Cambridge,1985. CR - M.A.Synder, Chebyshev methods in Numerical Approximation, Prentice Hall, Inc., London,1966. CR - X.Shang, D.Han,Numerical solution of Fredholm integral equations of the first kind by using Legendre multi-wavelets, Appl. Math. Comput., 191,440-444, 2007. CR - K.Malekneyad, S.Sohrabi, Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets, Appl. Math. Comput., 186,836-843, 2007. UR - https://dergipark.org.tr/tr/pub/erciyesfen/issue//269764 L1 - https://dergipark.org.tr/tr/download/article-file/236248 ER -