Analysis and numerical solution of singularly perturbed partial differential equations with large spatial delays and integral boundary conditions: applications in chemical and catalytic systems

IF 2 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2025-05-26 DOI:10.1007/s10910-025-01737-6

Parvin Kumari, Jesus Vigo-Aguiar, Garima Agarwal

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Abstract

This work proposes a hybrid numerical strategy to effectively solve the singularly perturbed partial differential equations (SPPDEs) with integral boundary conditions and substantial spatial delays. For the time discretization, the Crank-Nicolson scheme was chosen because of its stability and second-order precision. In order to maximize accuracy in the vicinity of layers coming from the tiny perturbation parameter and delay parameter, the computational implementation will be carried out using a non-uniform Shishkin-type mesh for spatial discretization using cubic spline interpolation. The approach is tested numerically to verify its robustness and efficiency with respect to integral boundary conditions and delayed feedback. Applications to reaction-diffusion systems, catalytic reactions in porous media, and transport-reaction dynamics in tubular reactors are presented to illustrate the effectiveness of the proposed approach.

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具有大空间延迟和积分边界条件的奇摄动偏微分方程的分析和数值解：在化学和催化系统中的应用

本文提出了一种混合数值策略来有效地求解具有积分边界条件和大量空间延迟的奇异摄动偏微分方程。对于时间离散，由于其稳定性和二阶精度，选择了Crank-Nicolson格式。为了使来自微小扰动参数和延迟参数的层附近的精度最大化，将使用非均匀shishkin型网格进行三次样条插值的空间离散化计算实现。数值实验验证了该方法在积分边界条件和延迟反馈条件下的鲁棒性和有效性。应用于反应扩散系统，多孔介质中的催化反应，以及管式反应器中的输运反应动力学，以说明所提出的方法的有效性。

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

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.