NSF-CBMS Regional Research Conference, Nonstandard Finite Difference Methods: Advances in Theory and Applications

NSF-CBMS 区域研究会议，非标准有限差分方法：理论与应用进展

• 批准号: 1933548
• 负责人: Dominic Clemence
• 金额: $ 3.5万
• 依托单位: North Carolina Agricultural & Technical State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1933548&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Research; Conference

This National Science Foundation award supports the 2020 NSF-CBMS conference "Nonstandard Finite Difference Methods: Advances in Theory and Applications" to be held July 20-24, 2020 at North Carolina A&T State University. The 5-day conference will feature Professor Ronald E. Mickens of Clark Atlanta University, who will deliver ten lectures on the topic, beginning with basic numerical motivations for the method, including theoretical exposition and various applications to differential equations models of diverse phenomena in the sciences, medicine, and engineering, and concluding with open problems. While the general scientific goal of the conference is the understanding and extensions of nonstandard finite difference methods (NSFD) methods that will emerge from the lectures and the discussion sessions, the human development goal is to introduce and encourage new researchers to this exciting field of research, with a focus on faculty and students from Historically Black Colleges and Universities and Minority Serving Institutes, whose activities are normally confined to teaching. The conference is intended to stimulate interest and activity in the study of NSFD methods and their applications, to be enabled by hands-on activities as well as panel discussions led by invited senior researchers on NSFD models in applications, graduate and undergraduate research projects, and a framework for future collaborations.The main conference lectures are designed to advance understanding and explore new frontiers in NSFD theory and applications of the methodology, which addresses the emergence of numerical instabilities and contrived chaotic behavior that is prevalent in standard finite difference models. Beginning with need for numerical methods for DEs, the lectures will introduce participants to the basic foundations and formulations of the NSFD methodology, discuss the state-of-the-art and latest advances in theory and applications, and summarize open problems as well as possible future directions in the field. Advances in theory will include explorations of potentially transformative concepts for generalized NSFD construction methods for systems of ordinary, partial, delay, and fractional differential equations. Advances in applications will be highlighted with various studies of engineering, science, and mathematical phenomena of classic or emerging interest modeled by the various classes of differential equations. The lectures presented by Professor Mickens, to be consolidated in a monograph, will unify these disparate research areas at their intersection and will serve as a resource to advance understanding, discovery, and inter-disciplinary collaboration in the mathematical sciences and other science and engineering disciplines. Further conference information will be available at http://www.ncat.edu/~math/cbms2020/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个国家科学基金会奖支持2020年NSF-CBMS会议“非标准有限差分方法：理论与应用的进展”将于2020年7月20日至24日在北卡罗来纳州AT州立大学举行。为期5天的会议将由罗纳德教授E。克拉克亚特兰大大学的Mickens，谁将提供十个讲座的主题，从基本的数值动机的方法，包括理论阐述和各种应用的微分方程模型的各种现象在科学，医学和工程，并与开放的问题结束。 虽然会议的总体科学目标是理解和扩展非标准有限差分法（NSFD）方法，这些方法将从讲座和讨论会中出现，但人类发展目标是介绍和鼓励新的研究人员进入这一令人兴奋的研究领域，重点是历史上黑人学院和大学以及少数民族服务机构的教师和学生，其活动通常限于教学。该会议旨在激发对NSFD方法及其应用研究的兴趣和活动，通过实践活动以及由受邀的高级研究人员领导的小组讨论来实现NSFD模型在应用，研究生和本科生研究项目，和未来合作的框架。主要的会议讲座旨在促进理解和探索新的前沿NSFD理论和应用，该方法，它解决了出现的数值不稳定性和人为的混沌行为，是普遍存在于标准的有限差分模型。从DE数值方法的需求开始，讲座将向参与者介绍NSFD方法的基本基础和公式，讨论理论和应用的最新进展，并总结开放问题以及该领域未来可能的方向。理论上的进展将包括探索潜在的变革概念，为系统的普通，部分，延迟和分数阶微分方程的广义NSFD建设方法。在应用方面的进展将突出与工程，科学和经典或新兴兴趣的数学现象的各种研究建模的各类微分方程。由米肯斯教授提出的讲座，将在一本专著中得到巩固，将这些不同的研究领域在其交叉点统一起来，并将作为一种资源，以促进理解，发现，以及在数学科学和其他科学和工程学科的跨学科合作。更多的会议信息将在www.example.com上提供http://www.ncat.edu/~math/cbms2020/This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。