A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation-Reference-Cited by-同舟云学术

A novel conservative numerical approximation scheme for the Rosenau-Kawahara equation

Published:2023-01-01 Issue:1 Volume:56 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Pan Xintian¹,Zhang Luming²

Affiliation:

1. School of Mathematics and Information Science, Weifang University , Weifang , 261061 , China

2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics , Nanjing , 210016 , China

Abstract

Abstract In this article, a numerical solution for the Rosenau-Kawahara equation is considered. A new conservative numerical approximation scheme is presented to solve the initial boundary value problem of the Rosenau-Kawahara equation, which preserves the original conservative properties. The proposed scheme is based on the finite difference method. The existence of the numerical solutions for the scheme has been shown by Browder fixed point theorem. The priori bound and error estimates, as well as the conservation of discrete mass and discrete energy for the finite difference solutions, are discussed. The discrepancies of discrete mass and energy are computed and shown by the curves of these quantities over time. Unconditional stability, second-order convergence, and uniqueness of the scheme are proved based on the discrete energy method. Numerical examples are given to show the effectiveness of the proposed scheme and confirm the theoretical analysis.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0204/pdf

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