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Journals / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 7 Issue: 1

New Exact and Numerical Experiments for the Caudrey-Dodd-Gibbon Equation

Seydi Battal Gazi Karakoç(Nevşehir Hacı Bektaş Veli University)0000-0002-2348-4170
Derya Yıldırım Sucu(NEVSEHIR HACI BEKTAS VELI UNIVERSITY)0000-0001-8396-8081
Pages
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Publication Date
2024-03-31
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Also, the obtained results indicate that our method is favourable for solving such problems.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, an exact and a numerical method namely direct algebraic method and collocation finite element method are proposed for solving soliton solutions of a special form of fifth-order KdV (fKdV) equation that is of particular importance: Caudrey-Dodd-Gibbon (CDG) equation.
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Key Findings & Data:The error norms $L_{2}$ and $L_{\infty }$ have been computed to control proficiency and conservation properties of the suggested algorithm.
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Conclusion & Impact:Also, the obtained results indicate that our method is favourable for solving such problems.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Caudrey-Dodd-Gibbon equation · collocation · direct algebraic method

Abstract

In this study, an exact and a numerical method namely direct algebraic method and collocation finite element method are proposed for solving soliton solutions of a special form of fifth-order KdV (fKdV) equation that is of particular importance: Caudrey-Dodd-Gibbon (CDG) equation. For these aims, homogeneous balance method and septic B-spline functions are used for exact and numerical solutions, respectively. Next, it is proved by applying von-Neumann stability analysis that the numerical method is unconditionally stable. The error norms $L_{2}$ and $L_{\infty }$ have been computed to control proficiency and conservation properties of the suggested algorithm. The obtained numerical results have been listed in the tables. The graphs are modelled so that easy visualization of properties of the problem. Also, the obtained results indicate that our method is favourable for solving such problems.

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Cite This Article

Karakoç, S. B. G., Sucu, D. Y. (2024). New Exact and Numerical Experiments for the Caudrey-Dodd-Gibbon Equation. Fundamental Journal of Mathematics and Applications, Volume: 7 Issue: 1. https://doi.org/10.33401/fujma.1389595

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