Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines

Murat Arı; Yılmaz Dereli

doi:10.47000/tjmcs.1851485

Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines

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.

Keywords

References

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Details

Primary Language

English

Subjects

Numerical and Computational Mathematics (Other)

Journal Section

Research Article

Authors

Murat Arı ^*
0000-0002-4039-5970
Türkiye

Yılmaz Dereli
0000-0003-0149-0542
Türkiye

Publication Date

June 30, 2026

Submission Date

December 29, 2025

Acceptance Date

February 4, 2026

Published in Issue

Year 2026 Volume: 18 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1851485

IZ

https://izlik.org/JA25UW46HJ

Cite

RIS / Bibtex

APA

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, 18(2), 450-460. https://doi.org/10.47000/tjmcs.1851485

AMA

1.Arı M, Dereli Y. Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines. TJMCS. 2026;18(2):450-460. doi:10.47000/tjmcs.1851485

Chicago

Arı, Murat, and Yılmaz Dereli. 2026. “Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines”. Turkish Journal of Mathematics and Computer Science 18 (2): 450-60. https://doi.org/10.47000/tjmcs.1851485.

EndNote

Arı M, Dereli Y (June 1, 2026) Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines. Turkish Journal of Mathematics and Computer Science 18 2 450–460.

IEEE

[1]M. Arı and Y. Dereli, “Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines”, TJMCS, vol. 18, no. 2, pp. 450–460, June 2026, doi: 10.47000/tjmcs.1851485.

ISNAD

Arı, Murat - Dereli, Yılmaz. “Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines”. Turkish Journal of Mathematics and Computer Science 18/2 (June 1, 2026): 450-460. https://doi.org/10.47000/tjmcs.1851485.

JAMA

1.Arı M, Dereli Y. Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines. TJMCS. 2026;18:450–460.

MLA

Arı, Murat, and Yılmaz Dereli. “Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 2, June 2026, pp. 450-6, doi:10.47000/tjmcs.1851485.

Vancouver

1.Murat Arı, Yılmaz Dereli. Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines. TJMCS. 2026 Jun. 1;18(2):450-6. doi:10.47000/tjmcs.1851485