Logaritmik tekil integro diferansiyel denklemlerin nümerik çözümleri

Yıl 2013, Cilt: 29 Sayı: 2, 101 - 109, 01.04.2013

Mustafa Gülsu Yalçın Öztürk Mehmet Sezer

Öz

Bu çalışmanın temel amacı karışık koşullar ile en genel halde verilen logaritmik tekil integro diferasiyel denklemlerin nümerik çözümleri için birinci tip Chebyshev polinomları yardımıyla bir yöntem geliştirmektir. Bu yöntem denklem çözümünün birinci tip Chebyshev polinomları cinsinden seriye açılma esasına dayanır. Logaritmik tekil integro diferansiyel denklemde bulunan fonksiyonların birinci tip Chebyshev serisine açılması ile elde edilen matris denklemi çözülerek Chebyshev katsayıları bulunmuştur. Öneri len yöntem için hata analizi ve yakınsaklık incelemesi yapılmıştır

Anahtar Kelimeler

Birinci tip Chebyshev polinomları, sıralama yöntemi, logaritmik tekil integral, Symm’s integral denklemi, yaklaşım yöntemleri

Numerical solution of Logaritmic singular integro differential equations

Öz

The main purpose of this article is to present an approximation method for logarithmic singular (Symm’s integral equation [1] integro - differential equations in the most general form under the mixed conditions in terms of the first kind Chebyshev polynomials. This method is based on the first - kind Chebyshev polynomials. The solut ion is obtained in terms of the first - kind Chebyshev polynomials. This scheme is based on taking the truncated the first - kind Chebyshev expansion of the function in the Logaritmic singular integro - differential equations. Hence, the result matrix equation c an be solved and the unknown the first - kind Chebyshev polynomial coefficients can be found approximately. The error analysis and convergence for the proposed method is also introduced.

Anahtar Kelimeler

The first-kind Chebyshev polynomial, collocation methods, logarithmic integral equation, Symm’s integral equation, approximation method

Kaynakça

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