Numerical analysis of a linear second-order finite difference scheme for space-fractional Allen–Cahn equations

IF 3.1 3区数学 Q1 MATHEMATICS

Advances in Difference Equations Pub Date : 2022-08-20 DOI:10.1186/s13662-022-03725-5

Kai Wang, Jundong Feng, Hongbo Chen, Changling Xu

引用次数: 0

Abstract

In this paper, we construct a new linear second-order finite difference scheme with two parameters for space-fractional Allen–Cahn equations. We first prove that the discrete maximum principle holds under reasonable constraints on time step size and coefficient of stabilized term. Secondly, we analyze the maximum-norm error. Thirdly, we can see that the proposed scheme is unconditionally energy-stable by defining the modified energy and selecting the appropriate parameters. Finally, two numerical examples are presented to verify the theoretical results.

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空间分数阶Allen-Cahn方程线性二阶有限差分格式的数值分析

本文构造了空间分数阶Allen-Cahn方程的一种新的线性二阶双参数有限差分格式。首先证明了在合理的时间步长和稳定项系数约束下，离散极大值原理成立。其次，分析了最大范数误差。第三，通过定义修正后的能量并选择合适的参数，可以看出所提方案是无条件能量稳定的。最后给出了两个数值算例来验证理论结果。

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

Advances in Difference Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

8.60

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.