Numerical simulation of the time fractional Gray-Scott model on 2D space domains using radial basis functions

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-01-27 DOI:10.1007/s10910-023-01571-8

Harshad Sakariya, Sushil Kumar

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Abstract

The Gray-Scott system describes one of the crucial components of the reaction-diffusion system. Its mathematical model has a couple of non-linear partial differential equations that are challenging to solve numerically. The present study is concerned with the numerical solution of the time-fractional Gray-Scott model in arbitrary-shaped domains utilizing the finite difference approximation and radial basis functions (RBFs) based collocation method for time and space directions, respectively. The patterns are created in the domains that denote the leftover chemical component concentrations at a specific time in the system. We also witness the effects of the time-fractional order \((\alpha )\) and diffusion constants (\(K_u\) and \(K_v\)) on the model. This study asserts that chemical reactions between two substances manifest chaotic and unpredictable behavior. Investigating the influence of time-fractional order introduces an intriguing avenue for exploring novel patterns and behaviors within this context. Furthermore, the proposed algorithm can be used to solve the model and generate novel patterns by altering the parameter values or geometric configurations in any space dimension.

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使用径向基函数对二维空间域上的时间分数格雷-斯科特模型进行数值模拟

格雷-斯科特系统描述了反应-扩散系统的一个重要组成部分。其数学模型包含几个非线性偏微分方程，数值求解具有挑战性。本研究采用有限差分近似法和基于径向基函数（RBFs）的时间和空间配位法，分别对任意形状域中的时间-分数 Gray-Scott 模型进行数值求解。在域中创建的模式表示系统中特定时间的剩余化学成分浓度。我们还见证了时间分阶（(\alpha )\）和扩散常数（\(K_u\) 和\(K_v\)）对模型的影响。这项研究认为，两种物质之间的化学反应表现出混沌和不可预测的行为。研究时间分数阶的影响为在此背景下探索新的模式和行为提供了一个有趣的途径。此外，所提出的算法可用于求解模型，并通过改变任意空间维度的参数值或几何配置生成新模式。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.