针对二阶 ODE 的新型高效四级隐式三角拟合修正 RKN

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

Journal of Computational Science Pub Date : 2024-06-22 DOI:10.1016/j.jocs.2024.102370

Bingzhen Chen , Yuna Zhao , Wenjuan Zhai

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引用次数: 0

摘要

本文研究了隐式 RKN 的构造。通过考虑对称、对称和三角拟合条件，我们最终得到了四个四级隐式积分器。对于新得到的方法，我们分析了它们的全局收敛性和稳定性。我们还对一些文献中常见的问题进行了数值实验。通过数值实验，我们发现新方法在精度和效率上都优于几种高效的 RKN 方法。

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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New efficient four-stage implicit trigonometrically fitted modified RKN for second-order ODEs

The construction of implicit RKN is investigated in this paper. We finally obtain four four-stages implicit integrators by considering the symmetric, symplectic, and trigonometric fitting conditions. For the new obtained methods, we analyze their global convergence and stability property. And we carry out numerical experiments on some commonly considered problems in the literature. In view of the numerical experiments, we observe that the new methods outperform several efficient RKN methods in terms of accuracy and efficiency.

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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).