Morgan-Voyce Polynomial Approach for Solution of High-Order Linear Differential-Difference Equations with Residual Error Estimation

Year 2016, Volume: 4 Issue: 1, 252 - 263, 31.01.2016

Bengü Türkyılmaz Burcu Gürbüz Mehmet Sezer

Abstract

The main aim of this study is to apply the Morgan-Voyce polynomials for the solution of high-order linear differential difference equations with functional arguments under initial boundary conditions. The technique we have used is essentially based on the truncated Morgan-Voyce series and its matrix representations along with collocation points. Also, by using the Mean-Value 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

Morgan- Voyce polynomials, Differential-difference equations, Collocation method, Matrix method, Error estimation, Residual function

Yüksek Mertebeden Lineer Diferansiyel Fark Denklemlerinin Hata Tahmini ile Morgan-Voyce Yaklaşımı

Abstract

Bu çalışmanın amacı, yüksek mertebeden fonkisyonel argümanlı lineer diferansiyel fark denklemlerinin başlangıç sınır koşulları altında Morgan- Voyce polinomlarına bağlı çözümlerini araştırmaktır. Kullanılan metot esas olarak kesilmiş Morgan- Voyce serilerinin ve sıralama noktalarına bağlı matris gösterimlerine dayalıdır. Ayrıca, Ortalama Değer Teoremi ve rezidüel fonksiyonu ile etkin bir hata tahmini yöntemi verilmektedir. Bazı örneklerle metotun geçerlilik ve uygulanabilirliği gösterilmektedir

Keywords

Morgan- Voyce polinomları, Diferansiyel-fark denklemleri, Kolokasyon metotu, Matris metotu, Hata tahmini, Rezidüel fonksiyon

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