A Robust and higher order numerical technique for a time-fractional equation with nonlocal condition

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-11-07 DOI:10.1007/s10910-024-01690-w

Komal Taneja, Komal Deswal, Devendra Kumar, J. Vigo-Aguiar

引用次数: 0

Abstract

This paper investigates a higher-order numerical technique for solving an inhomogeneous time fractional reaction-advection-diffusion equation with a nonlocal condition. The time-fractional operator involved here is the Caputo derivative. We discretize the Caputo derivative by an L1–2 formula, while the compact finite difference scheme approximates the spatial derivatives. The numerical approach is based on Taylor’s expansion combined with modified Gauss elimination. A thorough study demonstrates that the suggested approach is unconditionally stable. Tabular results show that the proposed scheme has fourth-order accuracy in space and \((3-\beta )\)-th-order accuracy in time. The numerical results of two test problems demonstrate the effectiveness and reliability of the theoretical estimates.

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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.