Kompleks düzlemin dairesel bölgesindeki lineer diferansiyel denklemlerin çözümleri için bir polinom yaklaşımı

Yıl 2012, Cilt: 28 Sayı: 1, 60 - 64, 01.02.2012

Mehmet Sezer Ayşegül Akyüz Daşcıoğlu

Öz

Bu makalede, dairesel bölgelerde yüksek mertebeden lineer kompleks diferansiyel denklemlerin çözümü için bir polinom yaklaşımı verilmektedir. Kullanılan bu sıralama yöntemi esas olarak denklemdeki bilinmeyen fonksiyon ve türev ifadelerinin kesilmiş Taylor seri temsillerinin matris gösterimlerine dayanır ki bunlar verilen bölgede tanımlanan sıralama noktalarını içerir. Yöntemin özelliklerini göstermek için karışık koşullu bazı sayısal örnekler verilmiştir.

Anahtar Kelimeler

Taylor sıralama yöntemi, Polinom yaklaşımı, Kompleks diferansiyel denklemler

A polynomial approximation for solutions of linear differential equations in circular domains of the complex plane

Öz

In this paper we give a polynomial approach to the solution of higher order linear complex differential equations in the circular domains. The used collocation method is essentially based on the matrix representations of the truncated Taylor series of the expressions in equation and their derivatives, which consist of collocation points defined in the given domains. Some numerical examples with the mixed conditions are given to show the properties of the technique.

Anahtar Kelimeler

Taylor Collocation method, Polynomial approximation, Complex differential equations

Kaynakça

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