Numerical solutions of one-dimensional Gelfand equation with fractional Laplacian

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-11-08 DOI:10.1007/s10910-024-01689-3

Lei Liu, Yufeng Xu

引用次数: 0

Abstract

In this paper, we discuss an efficient numerical method to obtain all solutions of fractional Gelfand equation with Dirichlet boundary condition. More precisely, we derive a good initial value motivated by the bifurcation curve of fractional Gelfand equation. It is obvious to see that the number of solutions depends on the value of parameter in fractional Gelfand equation. By collocation technique and finite difference method, numerical solutions can be found very quickly based on Newton iteration method with the aid of such initial guess. Numerical simulation for one-dimensional fractional Gelfand equation are provided, which demonstrates the accuracy and easy-to-implement of our algorithm.

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带分数拉普拉奇的一维格尔方方程的数值解法

在本文中，我们讨论了一种高效的数值方法，用于求取带 Dirichlet 边界条件的分数格尔方方程的所有解。更确切地说，我们从分数格尔方方程的分岔曲线出发，推导出了一个很好的初值。很明显，解的数量取决于分数格尔方方程的参数值。通过配位技术和有限差分法，在牛顿迭代法的基础上，借助这样的初始猜测，可以很快找到数值解。我们提供了一维分数格尔方方程的数值模拟，证明了我们算法的准确性和易用性。

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.