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Research Article | Open Access

Linear barycentric rational interpolation method for solving Kuramoto-Sivashinsky equation

School of Science, Shandong Jianzhu University, Jinan 250101, China
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Abstract

The Kuramoto-Sivashinsky (KS) equation being solved by the linear barycentric rational interpolation method (LBRIM) is presented. Three kinds of linearization schemes, direct linearization, partial linearization and Newton linearization, are presented to get the linear equation of the Kuramoto-Sivashinsky equation. Matrix equations of the discrete Kuramoto-Sivashinsky equation are also given. The convergence rate of LBRIM for solving the KS equation is also proved. At last, two examples are given to prove the theoretical analysis.

Keywords

barycentric rational interpolationcollocation methodKuramoto-Sivashinsky equationnon-linear PDE
CLC number: 65D32, 65D30, 65R20

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 16494-16510
DOI: 10.3934/math.2023843

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Cite this article:
Li J. Linear barycentric rational interpolation method for solving Kuramoto-Sivashinsky equation. AIMS Mathematics, 2023, 8(7): 16494-16510. https://doi.org/10.3934/math.2023843

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Received: 27 February 2023
Revised: 25 April 2023
Accepted: 04 May 2023
Published: 15 July 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)