Energy stability and error estimate of the RKMK2e scheme for the extended Fisher–Kolmogorov equation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-01-23 DOI:10.1016/j.apnum.2025.01.014

Haifeng Wang, Yan Wang, Hong Zhang, Songhe Song

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引用次数: 0

Abstract

In this paper, we develop a second-order accurate scheme for the extended Fisher–Kolmogorov (EFK) equation and investigate its global-in-time energy stability and convergence. The proposed scheme uses the Fourier spectral collocation method in space and the stabilization Runge–Kutta–Munthe–Kaas-2e (RKMK2e) method for temporal approximation. To demonstrate the global-in-time energy stability of the proposed scheme, we first verify that, under the assumption that all numerical solutions are uniformly bounded, the scheme is energy stable when using a sufficiently large stabilization parameter. Then, to establish the uniform-in-time boundedness of the numerical solutions, we fully utilize the nonlinear operator estimates and discrete Sobolev embedding in each stage of the scheme. Moreover, we conduct an optimal rate convergence analysis with a sufficient regularity assumption for the exact solution. Several numerical examples are presented to validate the accuracy, computational efficiency, and energy stability of the proposed scheme.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.