An \(\varrho \)-uniformly convergent technique for singularly perturbed problems, with an interior turning point occurring in chemical processes

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-11-11 DOI:10.1007/s10910-024-01692-8

Parvin Kumari, Devendra Kumar, Dumitru Baleanu

引用次数: 0

Abstract

A parameter-uniform solution is presented for singularly perturbed turning point problems with twin boundary layers. A fitted mesh is created in order to resolve the layers, and the provided equation is discretized using the cubic B-spline basis functions on this mesh. For the analytic solution and its derivatives, asymptotic bounds are provided. A brief analysis shows that the method is first-order precise in time and second-order accurate (up to a logarithm factor) in space, and that it is uniformly convergent regardless of the minuscule parameter. Two test problems are offered in order to verify the theoretical results.

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针对具有孪生边界层的奇异扰动转折点问题，提出了一种参数统一解法。为了解决层问题，创建了一个拟合网格，并在此网格上使用三次 B 样条基函数对所提供的方程进行离散化。对于解析解及其导数，提供了渐近边界。简要分析表明，该方法在时间上是一阶精确的，在空间上是二阶精确的（达到对数因子），而且无论微小参数如何，它都是均匀收敛的。为了验证理论结果，提供了两个测试问题。

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.