KARIŞIK ORANLI VE DEĞİŞKEN GECİKMELİ PANTOGRAF TİPİ FONKSİYONEL DİFERANSİYEL DENKLEMLER İÇİN GELİŞTİRİLMİŞ TAYLOR SIRALAMA METODU

Bu çalışmada karışık oranlı ve değişken gecikmeli yüksek mertebe lineer pantograf tip fonksiyonel diferansiyel denklemler geliştirilmiş Taylor matris metotla yaklaşık olarak çözülmüştür. Bu metotla fonksiyonel tip diferansiyel denklemler Taylor açılım metodu ile matris forma dönüştürülür. Problemler Taylor katsayılı cebirsel denklem kümesine indirgenir. Katsayılar belirlenerek yaklaşık çözümler hesaplanır. Ayrıca, metot için kalan fonksiyonlu hata analizi geliştirilmiştir. Metodun verimlilik ve uygulanabilirliğini göstermek için bazı açıklayıcı örnekler verilmiştir. Tüm hesaplamalar ve grafikler için Maple 15 programlama dili kullanılmıştır.

A MODIFIED TAYLOR COLLOCATION METHOD FOR PANTOGRAPH TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH HYBRID PROPORTIONAL AND VARIABLE DELAYS

In this work, high order pantograph type linear functional differential equations with hybrid proportional and variabledelays is approximately solved by the modified Taylor matrix method. With this method these functional type differentialequations are converted into the matrix form by the Taylor expansion method. The problems are reduced into a set ofalgebraic equations including Taylor coefficients. By determining the coefficients, the approximate solutions arecalculated. Also, an error analysis technique with residual function is developed for the presented method. Someillustrative examples are given to demonstrate the efficiency and applicability of the method. The computer algebraicsystem Maple 15 is used for all calculations and graphs.

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