Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations

Year 2024, Volume: 29 Issue: 1, 144 - 156, 30.04.2024

Demet Özdek

https://doi.org/10.53433/yyufbed.1330540

Abstract

In this study, we aim to solve Lane-Emden equations numerically by the Gegenbauer wavelet method. This method is mainly based on orthonormal Gegenbauer polynomials and takes advantage of orthonormality which reduces the computational cost. As a further advantage, Gegenbauer polynomials are associated with a real parameter allowing them to be defined as Legendre polynomials or Chebyshev polynomials for some values. Although this provides an opportunity to be able to analyze the problem under consideration from a wide point of view, the effect of the Gegenbauer parameter on the solution of Lane-Emden equations has not been studied so far. This study demonstrates the robustness of the Gegenbauer wavelet method on three problems of Lane-Emden equations considering different values of this parameter.

Keywords

Boundary value problems, Gegenbauer wavelets, Initial value problems, Lane-Emden equations

Lane-Emden Denklemlerinin Gegenbauer Dalgacık Çözümleri Üzerinde Gegenbauer Parametresinin Etkisi

Abstract

Bu çalışmada Lane-Emden denklemlerini Gegenbauer dalgacık yöntemi ile sayısal olarak çözmeyi amaçlıyoruz. Bu yöntem temel olarak ortonormal Gegenbauer polinomlarına dayanır ve hesaplama maliyetini azaltan ortonormallik avantajını kullanır. Diğer bir avantaj olarak, Gegenbauer polinomları, bazı değerleri için Legendre polinomları veya Chebyshev polinomları olarak tanımlanabilmelerini sağlayan reel bir parametre ile ilişkilendirilir. Bu durum, ele alınan problemi geniş bir bakış açısıyla analiz edebilmek için bir fırsat sağlasa da Gegenbauer parametresinin Lane-Emden denklemlerinin çözümü üzerindeki etkisi şimdiye kadar çalışılmamıştır. Bu çalışma, bu parametrenin farklı değerlerini dikkate alarak Gegenbauer dalgacık yönteminin Lane-Emden denklemlerinin üç problemi üzerindeki doğruluğunu göstermektedir.

Keywords

Başlangıç değer problemleri, Gegenbauer dalgacıkları, Lane-Emden denklemleri, Sınır değer problemleri

Supporting Institution

İzmir Ekonomi Üniversitesi

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