Numerical approach for time-fractional Burgers’ equation via a combination of Adams–Moulton and linearized technique

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-03-18 DOI:10.1007/s10910-024-01589-6

Yonghyeon Jeon, Sunyoung Bu

引用次数: 0

Abstract

Recently, fractional derivatives have become increasingly important for describing phenomena occurring in science and engineering fields. In this paper, we consider a numerical method for solving the fractional Burgers’ equations (FBEs), a vital topic in fractional partial differential equations. Due to the difficulty of the fractional derivatives, the nonlinear FBEs are linearized through the Rubin–Graves linearization scheme combined with the implicit the third-order Adams–Moulton scheme. Additionally, in the spatial direction of the FBEs, the fourth-order central finite difference scheme is used to obtain more accurate solutions. The convergence of the proposed scheme is theoretically and numerically analyzed. Also, the efficiency is demonstrated through several numerical experiments and compared with that of existing methods.

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结合亚当斯-莫尔顿和线性化技术的时间分数布尔格斯方程数值方法

近年来，分数导数在描述科学和工程领域的现象方面变得越来越重要。本文研究了求解分数伯格斯方程（FBE）的数值方法，这是分数偏微分方程的一个重要课题。由于分数导数的难度，非线性 FBE 通过 Rubin-Graves 线性化方案结合隐式三阶 Adams-Moulton 方案进行线性化。此外，在 FBE 的空间方向上，采用了四阶中心有限差分方案，以获得更精确的解。对所提方案的收敛性进行了理论和数值分析。同时，通过几个数值实验证明了其效率，并与现有方法进行了比较。

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.