Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials

Ayşe ANAPALI, (Muğla Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Muğla, Türkiye)
Yalçın ÖZTÜRK, (Muğla Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Muğla, Türkiye)
Mustafa GÜLSU (Muğla Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Muğla, Türkiye)
Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi
3 1
Yıl: 2015 Cilt: 15 Sayı: 2 Sayfa Aralığı: 136 - 146 Metin Dili: Türkçe İndeks Tarihi: 29-07-2022

Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials

Öz:
Bu çalışmanın amacı linear terim içeren Duffing‐van der Pol denkleminin shifted Chebyshev polinomları yardımı ile yaklaşık çözümlerini sunmaktır. Bu amaçla Chebyshev sıralama metodu verilmiştir. Metodun ana karekteristiği verilen denklemi kesilmiş  Chebyshev serisinin katasyılarının içeren bir denklem sistemine indirgemesidir. Bu sistem çözülerek kesilmiş  Chebyshev serisinin katsayıları bulunur. Dolayısıyla yaklaşık çözüm elde edilir. Ayrıca, metodun uygulanabilirlini göstermek için örnekler sunulmuştur.
Anahtar Kelime:

Lineer İntegral Terim İçeren Duffing Denkleminin Shifted Chebyshev Polinomları ile Nümerik Çözümleri

Öz:
The purpose of this study is to give a shifted Chebyshev polynomial approximation for the solution of Duffing‐van der Pol equation involving linear integral term (DEILI). For this purpose, a new Chebyshev collocation method is introduced. This method is based on taking the truncated shifted Chebyshev expansion of the function. This method based on first taking the truncated Chebyshev series of the solution function in the DEILI and then, transforms DEILI and given conditions into a matrix equation and then, we have the system of nonlinear algebraic equation using collocation points. Then, solving the system of algebraic equations we have the coefficients of the truncated Chebyshev series. In addition, examples that illustrate the pertinent features of the method are presented, and the results of study are discussed.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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APA ANAPALI A, Öztürk Y, GÜLSU M (2015). Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. , 136 - 146.
Chicago ANAPALI Ayşe,Öztürk Yalçın,GÜLSU Mustafa Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. (2015): 136 - 146.
MLA ANAPALI Ayşe,Öztürk Yalçın,GÜLSU Mustafa Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. , 2015, ss.136 - 146.
AMA ANAPALI A,Öztürk Y,GÜLSU M Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. . 2015; 136 - 146.
Vancouver ANAPALI A,Öztürk Y,GÜLSU M Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. . 2015; 136 - 146.
IEEE ANAPALI A,Öztürk Y,GÜLSU M "Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials." , ss.136 - 146, 2015.
ISNAD ANAPALI, Ayşe vd. "Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials". (2015), 136-146.
APA ANAPALI A, Öztürk Y, GÜLSU M (2015). Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 15(2), 136 - 146.
Chicago ANAPALI Ayşe,Öztürk Yalçın,GÜLSU Mustafa Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 15, no.2 (2015): 136 - 146.
MLA ANAPALI Ayşe,Öztürk Yalçın,GÜLSU Mustafa Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, vol.15, no.2, 2015, ss.136 - 146.
AMA ANAPALI A,Öztürk Y,GÜLSU M Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi. 2015; 15(2): 136 - 146.
Vancouver ANAPALI A,Öztürk Y,GÜLSU M Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi. 2015; 15(2): 136 - 146.
IEEE ANAPALI A,Öztürk Y,GÜLSU M "Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials." Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 15, ss.136 - 146, 2015.
ISNAD ANAPALI, Ayşe vd. "Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials". Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 15/2 (2015), 136-146.
Sayfa Oluşturulma Tarihi
09-05-2024 5:12

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