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Journals / Turkish Journal of Mathematics / 2018 / Cilt: 42 - Sayı: 1

An effective application of differential quadrature method based on modi edcubic B-splines to numerical solutions of the KdV equation

Ali BAŞHAN
Pages
373–394
Publication Date
2022-11-03
DOI
—
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AI Summary & Key Takeaways

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

Stabilityanalysis of the present method is also given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, numerical solutions of the third-order nonlinear Korteweg{de Vries (KdV) equation are obtainedvia differential quadrature method based on modi ed cubic B-splines.
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Key Findings & Data:To show theaccuracy of the proposed method,L2andL1error norms of the problem, which has an analytical solution, and threelowest invariants are calculated and reported.
💡
Conclusion & Impact:Stabilityanalysis of the present method is also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, numerical solutions of the third-order nonlinear Korteweg{de Vries (KdV) equation are obtainedvia differential quadrature method based on modi ed cubic B-splines. Five different problems are solved. To show theaccuracy of the proposed method,L2andL1error norms of the problem, which has an analytical solution, and threelowest invariants are calculated and reported. The obtained solutions are compared with some earlier works. Stabilityanalysis of the present method is also given.

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Cite This Article

BAŞHAN, A. (2022). An effective application of differential quadrature method based on modi edcubic B-splines to numerical solutions of the KdV equation. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 1, 373–394. https://ajindex.com/articles/604580

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