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Journals / Turkish Journal of Mathematics / 2018 / Cilt: 42 - Sayı: 3

Convergence analysis and numerical solution of the Benjamin–Bona–Mahony equation by Lie–Trotter splitting

Nurcan GÜCÜYENEN KAYMAK
Gamze TANOĞLU
Muaz SEYDAOĞLU
Fatma ZÜRNACI
Pages
1471–1483
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

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

Finally, to confirm the expected convergence order, numericalexamples are studied.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, an operator splitting method is used to analyze nonlinear Benjamin–Bona–Mahony-typeequations.
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Key Findings & Data:We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie–Trottersplitting is applied to the equation.
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Conclusion & Impact:Finally, to confirm the expected convergence order, numericalexamples are studied.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, an operator splitting method is used to analyze nonlinear Benjamin–Bona–Mahony-typeequations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie–Trottersplitting is applied to the equation. The local error bounds are obtained by using the approach based on the differentialtheory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global errorestimate is obtained via Lady Windermere’s fan argument. Finally, to confirm the expected convergence order, numericalexamples are studied.

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Cite This Article

KAYMAK, N. G., TANOĞLU, G., SEYDAOĞLU, M., ZÜRNACI, F. (2022). Convergence analysis and numerical solution of the Benjamin–Bona–Mahony equation by Lie–Trotter splitting. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 3, 1471–1483. https://ajindex.com/articles/607778

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