Yüksek Mertebeden Lineer Diferansiyel Fark Denklemlerinin Rezidüel Hata Tahminiyle Çözümü için Boubaker Polinom Yaklaşımı

Year 2016, Volume: 1 Issue: 1, 12 - 27, 27.12.2016

Salih Yalçınbaş , Mehmet Sezer , Elif Zinnur Aykutalp

Abstract

Bu
çalışmanın temel amacı başlangıç-sınır koşulları altında fonksiyonel argümentli
yüksek mertebeden lineer diferansiyel-fark denklemlerinin çözümü için Boubaker
polinomlarını uygulamaktır. Kullandığımız teknik, aslında sıralama noktaları ile
birlikte kesilmiş Boubaker serisine ve bunların matris gösterimlerine
dayandırılır. Ayrıca, Ortalama-Değer Teoremini ve rezidüel fonksiyonu
kullanarak, etkili bir hata tahmin tekniği önerilir; metodun etkinliğini ve
uygulanabilirliğini göstermek için  bazı
açıklayıcı örnekler sunulur.

Keywords

Boubaker Polinomları ve Serileri, Sıralama Noktaları, Diferansiyel Fark Denklemleri, Matris Metodu

Boubaker Polynomial Approach for Solving High-Order Linear Differential-Difference Equations with Residual Error Estimation

Abstract

The main aim of this study is to apply the Boubaker polynomials for the
solution of high-order linear differential-difference equations with functional
arguments under the initial-boundary conditions. The technique we have used is
essentially based on the truncated Boubaker series and its matrix
representations together with collocation points. Also, by using the Mean-Volue
Theorem and residual function, an efficient error estimation technique is
proposed and some illustrative examples are presented to demonstrate the
validity and applicability of the method.

Keywords

Boubaker Polynomials and Series, Collocation Points, Differential-Difference Equations, Matrix Method

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