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Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi / 2026 / Cilt: 31 Sayı: 1

A Petrov-Galerkin finite element method for the numerical solution of the KdV-Burgers' equation

Petrov- Galerkin sonlu eleman yöntemi ile KdV-Burgers' denkleminin nümerik çözümü

Seydi Battal Gazi Karakoç
Ali Rıza Aba(Nevsehir Haci Bektas Veli University, Nevsehir, Turkey)
Pages
24–31
Publication Date
2015-02-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The obtained numerical results are compared with results given in the literature and shown graphically.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a Petrov-Galerkin finite element method, in which the element shape functions are cubic and weight functions are quadratic B-splines, is implemented to find the numerical solution of the Korteweg-de Vries-Burgers'(KdVB) equation.
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Key Findings & Data:Accuracy of the presented method is demonstrated by three test problems.
💡
Conclusion & Impact:The obtained numerical results are compared with results given in the literature and shown graphically.
🔬Design:Makale
📍Scope:Comprehensive Sample
⚙️Variables:KdVB dnenklemi · Sonlu eleman metodu · Petrov- Galerkin

Abstract

In this study, a Petrov-Galerkin finite element method, in which the element shape functions are cubic and weight functions are quadratic B-splines, is implemented to find the numerical solution of the Korteweg-de Vries-Burgers'(KdVB) equation. Accuracy of the presented method is demonstrated by three test problems. The obtained numerical results are compared with results given in the literature and shown graphically.

Özet

Bu bölümde KdVB denkleminin sayısal çözümleri şekil fonksiyonları kübik, ağırlık fonksiyonları kuadratik B-spline fonksiyonları alınarak Petrov-Galerkin yöntemi ile elde edildi. Yöntemin doğruluğu ve etkinliği için üç tane test problemi ele alındı. Elde edilen denklem sistemleri Thomas algoritması ile çözüldü. Ayrıca elde edilen sayısal sonuçlar literatürdeki sonuçlar ile karşılaştırıldı.

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Cite This Article

Karakoç, S. B. G., Aba, A. R. (2015). A Petrov-Galerkin finite element method for the numerical solution of the KdV-Burgers' equation. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, Cilt: 31 Sayı: 1, 24–31. https://ajindex.com/articles/1267041

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