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

Demet Özdek

doi:10.53433/yyufbed.1330540

TR EN

Lane-Emden Denklemlerinin Gegenbauer Dalgacık Çözümleri Üzerinde Gegenbauer Parametresinin Etkisi

Öz

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.

Anahtar Kelimeler

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

Destekleyen Kurum

İzmir Ekonomi Üniversitesi

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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Ayrıntılar

Birincil Dil

İngilizce

Konular

Sayısal Analiz, Sayısal ve Hesaplamalı Matematik (Diğer)

Bölüm

Araştırma Makalesi

Yazarlar

Demet Özdek ^*
0000-0003-3877-6739
Türkiye

Yayımlanma Tarihi

30 Nisan 2024

Gönderilme Tarihi

20 Temmuz 2023

Kabul Tarihi

22 Kasım 2023

Yayımlandığı Sayı

Yıl 2024 Cilt: 29 Sayı: 1

DOI

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

IZ

https://izlik.org/JA82UH88BY

APA

Özdek, D. (2024). Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 29(1), 144-156. https://doi.org/10.53433/yyufbed.1330540

AMA

1.Özdek D. Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations. YYUFBED. 2024;29(1):144-156. doi:10.53433/yyufbed.1330540

Chicago

Özdek, Demet. 2024. “Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29 (1): 144-56. https://doi.org/10.53433/yyufbed.1330540.

EndNote

Özdek D (01 Nisan 2024) Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29 1 144–156.

IEEE

[1]D. Özdek, “Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations”, YYUFBED, c. 29, sy 1, ss. 144–156, Nis. 2024, doi: 10.53433/yyufbed.1330540.

ISNAD

Özdek, Demet. “Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29/1 (01 Nisan 2024): 144-156. https://doi.org/10.53433/yyufbed.1330540.

JAMA

1.Özdek D. Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations. YYUFBED. 2024;29:144–156.

MLA

Özdek, Demet. “Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 29, sy 1, Nisan 2024, ss. 144-56, doi:10.53433/yyufbed.1330540.

Vancouver

1.Demet Özdek. Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations. YYUFBED. 01 Nisan 2024;29(1):144-56. doi:10.53433/yyufbed.1330540

Lane-Emden Denklemlerinin Gegenbauer Dalgacık Çözümleri Üzerinde Gegenbauer Parametresinin Etkisi

Öz

Anahtar Kelimeler

Destekleyen Kurum

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

Öz

Anahtar Kelimeler

Kaynakça

Ayrıntılar

Birincil Dil

Konular

Bölüm

Yazarlar

Yayımlanma Tarihi

Gönderilme Tarihi

Kabul Tarihi

Yayımlandığı Sayı

DOI

IZ

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