A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION

Murat Arı

doi:10.18038/estubtda.1743984

EN

A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION

Abstract

This study presents a robust numerical approach for solving the nonlinear Korteweg–de Vries–Burgers (KdVB) equation using the Cubic Hermite Collocation Method. The method employs piecewise cubic Hermite basis functions, which ensure both high-order accuracy and smooth derivative continuity across element boundaries. These features make the method particularly suitable for problems involving sharp gradients or smooth solution profiles. The proposed scheme is rigorously tested on a set of benchmark problems to demonstrate its effectiveness in accurately capturing the complex interplay between the dispersive and dissipative behavior inherent to the KdVB equation. Numerical results which are given with L_2 and L_∞ error norms exhibit excellent agreement with known analytical or previously published numerical solutions, and confirm the method’s stability, efficiency, and reliability. In addition, graphical representations of the numerical solutions are provided to visually illustrate the method’s performance. Due to its flexibility, accuracy, and ease of implementation, the Cubic Hermite Collocation Method proves to be a promising and efficient alternative for the numerical solution of nonlinear PDEs with mixed physical effects.

Keywords

Korteweg–de Vries–Burgers equation, Cubic Hermite collocation method, Legendre roots, Chebyshev roots

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Numerical Analysis

Journal Section

Research Article

Authors

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

Publication Date

December 25, 2025

Submission Date

July 16, 2025

Acceptance Date

October 9, 2025

Published in Issue

Year 2025 Volume: 26 Number: 4

DOI

https://doi.org/10.18038/estubtda.1743984

IZ

https://izlik.org/JA56HN44UG

APA

Arı, M. (2025). A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, 26(4), 445-459. https://doi.org/10.18038/estubtda.1743984

AMA

1.Arı M. A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION. Estuscience - Se. 2025;26(4):445-459. doi:10.18038/estubtda.1743984

Chicago

Arı, Murat. 2025. “A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 26 (4): 445-59. https://doi.org/10.18038/estubtda.1743984.

EndNote

Arı M (December 1, 2025) A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 26 4 445–459.

IEEE

[1]M. Arı, “A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION”, Estuscience - Se, vol. 26, no. 4, pp. 445–459, Dec. 2025, doi: 10.18038/estubtda.1743984.

ISNAD

Arı, Murat. “A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 26/4 (December 1, 2025): 445-459. https://doi.org/10.18038/estubtda.1743984.

JAMA

1.Arı M. A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION. Estuscience - Se. 2025;26:445–459.

MLA

Arı, Murat. “A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION”. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 26, no. 4, Dec. 2025, pp. 445-59, doi:10.18038/estubtda.1743984.

Vancouver

1.Murat Arı. A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION. Estuscience - Se. 2025 Dec. 1;26(4):445-59. doi:10.18038/estubtda.1743984

Abstract

A CUBIC HERMITE COLLOCATION APPROACH FOR SOLVING THE KORTEWEG–DE VRIES–BURGERS EQUATION

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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