Numerical investigation of two fractional operators for time fractional delay differential equation

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-06-19 DOI:10.1007/s10910-024-01637-1

Reetika Chawla, Devendra Kumar, Dumitru Baleanu

引用次数: 0

Abstract

This article compared two high-order numerical schemes for convection-diffusion delay differential equation via two fractional operators with singular kernels. The objective is to present two effective schemes that give \((3-\alpha )\) and second order of accuracy in the time direction when \(\alpha \in (0,1)\) using Caputo and Modified Atangana-Baleanu Caputo derivatives, respectively. We also implemented a trigonometric spline technique in the space direction, giving second order of accuracy. Moreover, meticulous analysis shows these numerical schemes to be unconditionally stable and convergent. The efficiency and reliability of these schemes are illustrated by numerical experiments. The tabulated results obtained from test examples have also shown the comparison of these operators.

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时间分数延迟微分方程两个分数算子的数值研究

本文通过两个具有奇异核的分数算子，比较了对流扩散延迟微分方程的两种高阶数值方案。目的是提出两种有效的方案，分别使用 Caputo 和 Modified Atangana-Baleanu Caputo 导数，当 \(\alpha \ in (0,1)\) 时，在时间方向上给出 \((3-\alpha )\) 和二阶精度。我们还在空间方向采用了三角样条线技术，从而获得了二阶精度。此外，细致的分析表明这些数值方案是无条件稳定和收敛的。我们通过数值实验说明了这些方案的效率和可靠性。从测试实例中获得的表列结果也显示了这些算子的可比性。

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.