Unconditional error analysis of weighted implicit-explicit virtual element method for nonlinear neutral delay-reaction–diffusion equation

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-10-09 DOI:10.1016/j.cnsns.2024.108384

Shanshan Peng , Yanping Chen

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引用次数: 0

Abstract

In this paper, we develop a virtual element method in space for the nonlinear neutral delay-reaction–diffusion equation, while a weighted implicit-explicit scheme is utilized in time. The nonlinear term is adopted by using the Newton linearized method. The calculation efficiency is improved using an implicit scheme to analyze linear terms and an explicit scheme to deal with nonlinear terms. Then, the time–space error splitting technique and G-stability are creatively combined to rigorously analyze the unconditionally optimal convergence results of the numerical scheme without any restrictions on the mesh ratio. Finally, numerical examples on a set of polygonal meshes are provided to confirm the theoretical results. In particular, when the weighted parameter is taken

θ = \frac{1}{2}

(or

θ = 1

), the method degenerates into the Crank–Nicolson (or second-order backward differential formula (BDF2)) scheme.

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非线性中性延迟-反应-扩散方程的加权隐式-显式虚拟元素法的无条件误差分析

本文针对非线性中性延迟-反应-扩散方程开发了一种空间虚拟元素方法，同时在时间上采用了加权隐式-显式方案。非线性项采用牛顿线性化方法。利用隐式方案分析线性项，利用显式方案处理非线性项，从而提高了计算效率。然后，创造性地将时空误差分割技术和 G 稳定性结合起来，严格分析了数值方案的无条件最优收敛结果，对网格比例没有任何限制。最后，提供了一组多边形网格的数值实例来证实理论结果。特别是当加权参数取θ=12（或θ=1）时，该方法退化为 Crank-Nicolson（或二阶后向微分公式（BDF2））方案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.