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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, to confirm the expected convergence order, numerical examples are studied.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations.
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Key Findings & Data:We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation.
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Conclusion & Impact:Finally, to confirm the expected convergence order, numerical examples are studied.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lie-Trotter splitting · convergence analysis · Benjamin-Bona-Mahony equation
Abstract
In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.
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Cite This Article
ZÜRNACI, F., KAYMAK, N. G., SEYDAOĞLU, M., TANOĞLU, G. (2018). 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/723122