Lucas Polynomial Approach for Second Order Nonlinear Differential Equations

Year 2020, Volume: 24 Issue: 1, 230 - 236, 20.04.2020

Sevin Gümgüm , Nurcan Baykuş-savaşaneril Ömür Kıvanç Kürkçü , Mehmet Sezer

https://doi.org/10.19113/sdufenbed.546847

Cited By: 5

Abstract

 This paper presents the Lucas polynomial solution of second-order nonlinear ordinary differential equations with mixed conditions. Lucas matrix method is based on collocation points together with truncated Lucas series. The main advantage of the method is that it has a simple structure to deal with the nonlinear algebraic system obtained from matrix relations. The method is applied to four problems. In the first two problems, exact solutions are obtained. The last two problems, Bratu and Duffing equations are solved numerically; the results are compared with the exact solutions and some other numerical solutions. It is observed that the application of the method results in either the exact or accurate numerical solutions.

Keywords

Lucas polynomial, Operational matrices, Collocation points

İkinci Mertebeden Doğrusal Olmayan Diferansiyel Denklemler için Lucas Polinom Yaklaşımı

Abstract

Bu makale, karışık koşullar altında ikinci mertebeden doğrusal olmayan adi diferansiyel denklemlerin Lucas polinom çözümünü oluşturur. Lucas matris yöntemi sıralama noktaları ile birlikte sınırlandırılmış Lucas serisine dayanmaktadır. Yöntemin en büyük avantajı matris bağıntılarında elde edilen doğrusal olmayan cebirsel sistemi ele almak için basit bir yapıya sahip olmasıdır. Yöntem dört probleme uygulanır. İlk iki problemde, tam çözümler elde edilir. Son iki problemde Bratu ve Duffing denklemleri sayısal olarak çözülür; sonuçlar, tam çözümler ve diğer bazı sayısal çözümler ile karşılaştırılır. Yöntemin uygulanması, tam ve doğru sayısal çözümler vermesine yol açtığı gözlemlenmektedir.

Keywords

Lucas polinomu, İşlevsel matrisler, Sıralama noktaları

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