艾伦-卡恩方程的近似分析和数值解法比较

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-23 DOI:10.1155/2024/8835138

S. Hussain, Fazal Haq, Abdullah Shah, D. Abduvalieva, Ali Shokri

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引用次数: 0

摘要

由于存在立方项，艾伦-卡恩（AC）方程是一个高度非线性的方程，而且非常僵硬；因此，要找到其闭合形式的精确解析解并不容易。在本研究中，我们研究了 AC 方程的近似解析解。在这里，我们使用变分迭代法（VIM）来寻找交流方程的近似解析解。所得结果与双曲函数解法和行波解法进行了比较。我们还将所得结果与使用有限差分法（FDM）获得的数值解进行了比较。绝对误差分析表用于验证序列解。发现 VIM 获得的收敛级数解与分析解和数值解非常一致。

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Comparison of Approximate Analytical and Numerical Solutions of the Allen Cahn Equation

Allen Cahn (AC) equation is highly nonlinear due to the presence of cubic term and also very stiff; therefore, it is not easy to find its exact analytical solution in the closed form. In the present work, an approximate analytical solution of the AC equation has been investigated. Here, we used the variational iteration method (VIM) to find approximate analytical solution for AC equation. The obtained results are compared with the hyperbolic function solution and traveling wave solution. Results are also compared with the numerical solution obtained by using the finite difference method (FDM). Absolute error analysis tables are used to validate the series solution. A convergent series solution obtained by VIM is found to be in a good agreement with the analytical and numerical solutions.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.