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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Stability analysis of the present method is also given.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, numerical solutions of the third-order nonlinear Korteweg--de Vries (KdV) equation are obtained via differential quadrature method based on modified cubic B-splines.
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Key Findings & Data:To show the accuracy of the proposed method, $L_{2}$ and $L_{\infty }$ error norms of the problem, which has an analytical solution, and three lowest invariants are calculated and reported.
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Conclusion & Impact:Stability analysis of the present method is also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:KdV equation · differential quadrature method · modified cubic B-splines
Abstract
In this study, numerical solutions of the third-order nonlinear Korteweg--de Vries (KdV) equation are obtained via differential quadrature method based on modified cubic B-splines. Five different problems are solved. To show the accuracy of the proposed method, $L_{2}$ and $L_{\infty }$ error norms of the problem, which has an analytical solution, and three lowest invariants are calculated and reported. The obtained solutions are compared with some earlier works. Stability analysis of the present method is also given.
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Cite This Article
BAŞHAN, A. (2018). An effective application of differential quadrature method based on modified cubic B-splines to numerical solutions of the KdV equation. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 1, 373–394. https://ajindex.com/articles/723148