Chebyshev polynomial approximation for solving the second kind linear fredholm

Yıl 2010, Cilt: 26 Sayı: 3, 203 - 216, 01.06.2010

Mustafa Gülsu Yalçın Öztürk

Öz

The purpose of this study is to give a Chebyshev polynomial approximation for the solution of the second kind of Linear Fredholm integral equation. For this purpose, a new Chebyshev matrix method is introduced. This method is based on taking the truncated Chebyshev expansion of the function in the integral equations. Hence, the result matrix equation can be solved and the unknown Chebyshev coefficients can be found approximately. In addition, examples that illustrate the pertinent features of the method are presented, and the results of study are discussed.

Anahtar Kelimeler

Chebyshev polynomials, Chebyshev series, Chebyshev polynomial solutions, Fredholm integral equations, approximation method

İkinci tip lineer fredholm integral denklemlerinin chebyshev polinom yaklaşımları

Öz

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.

Anahtar Kelimeler

Chebyshev polinomları, Chebyshev serileri, Chebyshev polinom çözümleri, Fredholm integral denklemi, Yaklaşım metodları

Kaynakça

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