Optimal error estimates of second-order weighted virtual element method for nonlinear coupled prey–predator equation

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-03-06 DOI:10.1016/j.cam.2025.116617

Yanping Chen , Shanshan Peng

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引用次数: 0

Abstract

In this paper, we develop a numerical method for solving the nonlinear coupled prey–predator equation on arbitrary polygonal meshes, employing the virtual element method for spatial discretization and a second-order weighted method for temporal discretization. We rigorously establish the existence, uniqueness and convergence of solutions using Schaefer’s fixed point theorem. Moreover, we derive an optimal error estimate in the

H^{1}

-norm that is independent of any spatial–temporal grid ratio constraints. This approach eliminates the need for the time semi-discrete system that would otherwise be introduced by temporal–spatial error splitting techniques, thereby streamlining the computational process. By adjusting the weighted parameter

θ

, the second-order weighted scheme seamlessly transitions to classic methods such as Crank–Nicolson (

θ = 0.5

) and two-step backward differentiation formula method (

θ = 1

). Finally, numerical experiments confirm the validity of our theoretical results.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.