Mehmet SEZER, Bekir TANAY, Mustafa GÜLSU

EĞİŞKEN KATSAYILI YÜKSEK MERTEBEDEN LİNEER COMPLEX DİFERANSİYEL DENKLEMLERİN DAİRESEL BİR BÖLGEDE POLİNOM ÇÖZÜMLERİ

Bu çalışmada dairesel bir bölgede karışık koşullar altında değişken katsayılı yüksek mertebeden lineer complex diferansiyel denklemlerin Taylor matris yöntemi ile nümerik çözümlerinin bulunması amaçlanmıştır. Belirtilen yöntem denklemdeki fonksiyonların kesilmiş Taylor polinomlarının matris formlarının denklemde yerine konması esasına dayanır. Böylece denklem ve koşullar matris denklemine dönüştürülür. Bu denklemlerin çözümleri Taylor polinomlarının katsayılarını oluştururlar.Yöntemin uygulaması çeşitli örneklerle açıklanmış ve sonuçlar tartışılmıştır.

Anahtar Kelimeler:

Taylor yaklaşımları, Complex diferansiyel denklemler, Taylor matris yöntemi

A POLYNOMIAL APPROACH FOR SOLVING HIGH-ORDER LINEAR COMPLEX DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS IN DISC

The purpose of this study is to give a Taylor matrix method for approximately solving the high-order linear complex differential equations with variable coefficients under the mixed conditions in a circular domain. The method is based on first taking the truncated Taylor expansions of the expressions in equation and then substituting their matrix forms into the given equation. Hence the differential equation and conditions are transformed to the matrix equations. The solution of these equations yields the unknown Taylor coefficients of the solution function. To illustrate the pertinent features of the method, examples are presented and results are compared

Keywords:

Taylor approximation, Complex differential equations, Taylor matrix method,

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