Nonstandard finite difference schemes for linear and non-linear Fokker–Planck equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-23 DOI:10.1007/s10665-024-10346-2

A. S. Neena, Dominic P. Clemence-Mkhope, Ashish Awasthi

引用次数: 0

Abstract

The goal of this paper is to develop a nonstandard finite difference-based numerical technique for solving the one-dimensional linear and non-linear Fokker–Planck equations. Characteristics of the nonstandard finite difference method are presented to understand the development of the proposed method. Conditions for the dynamic consistency of positivity and stability of the schemes are obtained. Numerical experiments have been carried out to demonstrate the competitiveness of the proposed methods in comparison to some existing standard methods. In support of the proposed method and analysis, the \(l_2\) and \(l_\infty \) errors are also presented.

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线性和非线性福克-普朗克方程的非标准有限差分方案

本文旨在开发一种基于非标准有限差分的数值技术，用于求解一维线性和非线性福克-普朗克方程。本文介绍了非标准有限差分法的特点，以便理解所提议方法的发展。此外，还提出了方案正负动态一致性和稳定性的条件。通过数值实验证明了所提方法与一些现有标准方法的竞争力。为了支持所提出的方法和分析，还提出了 \(l_2\) 和 \(l\infty \) 误差。

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

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.