A local discontinuous Galerkin method for the Novikov equation-Reference-Cited by-同舟云学术

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A local discontinuous Galerkin method for the Novikov equation

Published:2024-09-06 Issue: Volume: Page:
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Tao Qi,Chang Xiang-Ke,Liu Yong,Shu Chi-Wang

Abstract

In this paper, we propose a local discontinuous Galerkin (LDG) method for the Novikov equation that contains cubic nonlinear high-order derivatives. Flux correction techniques are used to ensure the stability of the numerical scheme. The H 1 H^1 -norm stability of the general solution and the error estimate for smooth solutions without using any priori assumptions are presented. Numerical examples demonstrate the accuracy and capability of the LDG method for solving the Novikov equation.

Funder

National Natural Science Foundation of China

Publisher

American Mathematical Society (AMS)

Link

https://www.ams.org/mcom/0000-000-00/S0025-5718-2024-04018-8/mcom4018_AM.pdf

Reference49 articles.

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3. Hermite-Padé approximations with Pfaffian structures: Novikov peakon equation and integrable lattices;Chang, Xiang-Ke;Adv. Math.,2022

4. An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type;Chang, Xiang-Ke;Adv. Math.,2018

5. On the conservative finite difference scheme for the Novikov equation;Chen, Wenxia;Int. J. Nonlinear Sci.,2017

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