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Journals / Sakarya University Journal of Science / 2018 / Volume: 22 Issue: 6

Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method

Gardner Denkleminin Trigonometrik Kuintik B-spline Kolokasyon Yöntemi ile Nümerik Çözümleri

Özlem Ersoy Hepson
Pages
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Publication Date
2018-12-01
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AI Summary & Key Takeaways

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

Thus the Gardner equation turns into a penta diagonoal matrix equation and the Thomas algorithm is applied.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The main purpose of this paper is to get the numerical solutions of the Gardner equation which are widely used in various disciplines.
📊
Key Findings & Data:For this purpose, the time integration of the system is achieved by the classical Crank-Nicolson method owing to its large stability region.
💡
Conclusion & Impact:Thus the Gardner equation turns into a penta diagonoal matrix equation and the Thomas algorithm is applied.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Gardner Equation · trigonometric quintic B-spline · collocation

Abstract

The main purpose of this paper is to get the numerical solutions of the Gardner equation which are widely used in various disciplines. For this purpose, the time integration of the system is achieved by the classical Crank-Nicolson method owing to its large stability region. Space discretization is done by using the trigonometric quintic B-spline functions. Thus the Gardner equation turns into a penta diagonoal matrix equation and the Thomas algorithm is applied.

Özet

Bu çalışmanın amacı çeşitli disiplinlerde sıkça kullanılan Gardner denkleminin nümerik çözümlerini elde etmektir. Bu amaç için geniş kararlılık bölgesine sahip olmasından dolayı klasik Crank-Nicolson yöntemi ile zaman integrasyonu yapılmıştır. Konum ayrıştırması ise trigonometrik quintik B-spline fonksiyonları kullanılarak yapılmıştır. Bu yüzden Gardner denklemi beş bant matris sistemine dönüştürülmüş ve Thomas algoritması uygulanmıştır.

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Cite This Article

Hepson, Ö. E. (2018). Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method. Sakarya University Journal of Science, Volume: 22 Issue: 6. https://doi.org/10.16984/saufenbilder.342571

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