An efficient 6th-order compact difference scheme with error estimation for nonlocal Lane–Emden equation

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science Pub Date : 2025-02-01 DOI:10.1016/j.jocs.2025.102529

Nirupam Sahoo, Randhir Singh

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引用次数: 0

Abstract

In this manuscript, we present a new and efficient 6th-order compact difference method for solving the nonlocal Lane–Emden equation. This method effectively addresses singular-type problems without the need to modify or remove the singularities. To achieve this, we construct a uniform mesh across the domain and develop a new sixth-order discrete method that approximates the derivatives, transforming the differential equation into a system of equations. Use Newton or any iterative technique to obtain the numerical solution of the system of equations. Our new scheme efficiently handles the singularity at

t = 0

. Additionally, we conduct a mathematical analysis of the method’s consistency, stability, error bounds, and convergence rate. We also include several numerical problems from the existing literature to demonstrate the accuracy, efficiency, and applicability of the proposed scheme. Also, compare the numerical approximations with the existing recent techniques. The newly proposed scheme offers 6th-order accuracy using a small-size matrix and delivers better numerical results than the existing methods.

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非局部Lane-Emden方程的一种有效的带误差估计的六阶紧凑差分格式

本文给出了求解非局部Lane-Emden方程的一种新的、有效的6阶紧致差分法。该方法有效地解决了奇异型问题，而不需要修改或去除奇异点。为了实现这一目标，我们构建了一个跨域的均匀网格，并开发了一种新的六阶离散方法来逼近导数，将微分方程转换为方程组。使用牛顿或任何迭代技术来获得方程组的数值解。我们的新方案有效地处理了t=0处的奇点。此外，我们还对该方法的一致性、稳定性、误差范围和收敛速度进行了数学分析。我们还从现有文献中列举了几个数值问题来证明所提出方案的准确性、效率和适用性。同时，将数值近似与现有的最新技术进行比较。新提出的方案使用小尺寸矩阵提供6阶精度，并提供比现有方法更好的数值结果。

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 Computational Science COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-COMPUTER SCIENCE, THEORY & METHODS

CiteScore

5.50

自引率

3.00%

发文量

227

审稿时长

41 days

期刊介绍： Computational Science is a rapidly growing multi- and interdisciplinary field that uses advanced computing and data analysis to understand and solve complex problems. It has reached a level of predictive capability that now firmly complements the traditional pillars of experimentation and theory. The recent advances in experimental techniques such as detectors, on-line sensor networks and high-resolution imaging techniques, have opened up new windows into physical and biological processes at many levels of detail. The resulting data explosion allows for detailed data driven modeling and simulation. This new discipline in science combines computational thinking, modern computational methods, devices and collateral technologies to address problems far beyond the scope of traditional numerical methods. Computational science typically unifies three distinct elements: • Modeling, Algorithms and Simulations (e.g. numerical and non-numerical, discrete and continuous); • Software developed to solve science (e.g., biological, physical, and social), engineering, medicine, and humanities problems; • Computer and information science that develops and optimizes the advanced system hardware, software, networking, and data management components (e.g. problem solving environments).