A NEW MULTI-STEP BDF ENERGY STABLE TECHNIQUE FOR THE EXTENDED FISHER-KOLMOGOROV EQUATION-Reference-Cited by-同舟云学术

A NEW MULTI-STEP BDF ENERGY STABLE TECHNIQUE FOR THE EXTENDED FISHER-KOLMOGOROV EQUATION

Published:2024-02-23 Issue:1 Volume:29 Page:125-140
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Sun Qihang¹^ORCID,Hu Xiuling²,Li Xin³,Li Yang⁴,Zhang Luming⁵

Affiliation:

1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 211106 Nanjing, China; School of Information and Electrical engineering, Ludong University, 264025 Yantai, China

2. School of Mathematics and Statistics, Jiangsu Normal University, 221116 Xuzhou, China

3. School of Mathematics, Hefei University of Technology, 230009 Hefei, China

4. School of Mechatronic Engineering and Automation, Shanghai University, 200444 Shanghai, China

5. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 211106 Nanjing, China

Abstract

The multi-step backward difference formulas of order k (BDF-k) for 3 ≤ k ≤ 5 are proposed for solving the extended Fisher–Kolmogorov equation. Based upon the careful discrete gradient structures of the BDF-k formulas, the suggested numerical schemes are proved to preserve the energy dissipation laws at the discrete levels. The maximum norm priori estimate of the numerical solution is established by means of the energy stable property. With the help of discrete orthogonal convolution kernels techniques, the L2 norm error estimates of the implicit BDF-k schemes are established. Several numerical experiments are included to illustrate our theoretical results.

Publisher

Vilnius Gediminas Technical University

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