Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines

Murat Arı; Bahar Karaman; Yılmaz Dereli

doi:10.17776/csj.947289

EN

Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines

Abstract

This current investigation consists of the numerical solutions of the Generalized Rosenau-KdV equation by using the meshless kernel-based method of lines, which is a truly meshless method. The governing equation is a nonlinear partial differential equation but the use of the method of lines leads to an ordinary differential equation. Thus, the partial differential equation is replaced by the ordinary differential equation. The numerical efficiency of the used technique is tested by different numerical examples. Numerical values of error norms and physical invariants are compared with known values in the literature. Moreover, Multiquadric, Gaussian, and Wendland’s compactly supported functions are used in computations. It is seen that the used truly meshless method in computations is very effective with high accuracy and reliability.

Keywords

Generalized Rosenau-Kdv equation, Meshless Kernel-based method of lines, Radial basis function

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Murat Arı
0000-0002-4039-5970
Türkiye

Bahar Karaman ^*
0000-0001-6631-8562
Türkiye

Yılmaz Dereli
0000-0003-0149-0542
Türkiye

Publication Date

June 29, 2022

Submission Date

June 3, 2021

Acceptance Date

May 20, 2022

Published in Issue

Year 2022 Volume: 43 Number: 2

DOI

https://doi.org/10.17776/csj.947289

IZ

https://izlik.org/JA99NM66BU

APA

Arı, M., Karaman, B., & Dereli, Y. (2022). Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines. Cumhuriyet Science Journal, 43(2), 321-326. https://doi.org/10.17776/csj.947289

AMA

1.Arı M, Karaman B, Dereli Y. Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines. CSJ. 2022;43(2):321-326. doi:10.17776/csj.947289

Chicago

Arı, Murat, Bahar Karaman, and Yılmaz Dereli. 2022. “Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines”. Cumhuriyet Science Journal 43 (2): 321-26. https://doi.org/10.17776/csj.947289.

EndNote

Arı M, Karaman B, Dereli Y (June 1, 2022) Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines. Cumhuriyet Science Journal 43 2 321–326.

IEEE

[1]M. Arı, B. Karaman, and Y. Dereli, “Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines”, CSJ, vol. 43, no. 2, pp. 321–326, June 2022, doi: 10.17776/csj.947289.

ISNAD

Arı, Murat - Karaman, Bahar - Dereli, Yılmaz. “Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines”. Cumhuriyet Science Journal 43/2 (June 1, 2022): 321-326. https://doi.org/10.17776/csj.947289.

JAMA

1.Arı M, Karaman B, Dereli Y. Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines. CSJ. 2022;43:321–326.

MLA

Arı, Murat, et al. “Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines”. Cumhuriyet Science Journal, vol. 43, no. 2, June 2022, pp. 321-6, doi:10.17776/csj.947289.

Vancouver

1.Murat Arı, Bahar Karaman, Yılmaz Dereli. Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines. CSJ. 2022 Jun. 1;43(2):321-6. doi:10.17776/csj.947289

Cited By

An Artificial Neural Network Method for Simulating Soliton Propagation Based on the Rosenau-KdV-RLW Equation on Unbounded Domains

Mathematics

https://doi.org/10.3390/math13071036

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