The study concludes that the RBF-based MOL is a highly effective and reliable tool for simulating high-order nonlinear evolution equations.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:This paper presents a robust numerical scheme for solving the generalized Rosenau-Burgers equation using a meshless Method of Lines (MOL) approach based on Radial Basis Functions (RBFs).
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Temel Bulgular & Veri:The numerical results demonstrate that the proposed method achieves exceptional accuracy and, significantly outperforming existing results in the literature.
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Sonuç & Katkı:The study concludes that the RBF-based MOL is a highly effective and reliable tool for simulating high-order nonlinear evolution equations.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Radial basis function · method of lines · Rosenau-Burgers equation
Abstract
This paper presents a robust numerical scheme for solving the generalized Rosenau-Burgers equation using a meshless Method of Lines (MOL) approach based on Radial Basis Functions (RBFs). To evaluate the accuracy and stability of the proposed scheme, two distinct numerical examples are investigated, including the propagation of single solitary waves and their dynamic behavior under varying parameters. The numerical results demonstrate that the proposed method achieves exceptional accuracy and, significantly outperforming existing results in the literature. The study concludes that the RBF-based MOL is a highly effective and reliable tool for simulating high-order nonlinear evolution equations.
Arı, M., Dereli, Y. (2026). Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 2. https://doi.org/10.47000/tjmcs.1851485
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