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.

该国家科学基金会奖支持2020年NSF-CBMS会议“非标准有限差异方法：理论和应用的进步”将于7月20日至24日在北卡罗来纳州A＆T州立大学举行。为期5天的会议将以克拉克·亚特兰大大学（Clark Atlanta University）的罗纳德·E·米肯斯（Ronald E. 虽然该会议的一般科学目标是对非标准有限差异方法（NSFD）方法的理解和扩展，这些方法将从讲座和讨论会议中出现，但人类发展目标是向这一令人兴奋的研究领域介绍和鼓励新的研究人员，并侧重于历史悠久的黑人学院和大学的教职员工，并在企业中努力，他们的活动正常，他们的活动是正常的，他们的活动是正常的。该会议旨在刺激NSFD方法及其应用的兴趣和活动，该会议由动手活动以及由受邀高级研究人员在应用，研究生和本科研究项目中的NSFD模型的邀请高级研究人员领导的小组讨论来实现，以及未来的协作框架。在标准有限差异模型中普遍存在的数值不稳定性和人为的混乱行为。从需要DES的数值方法开始，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和最新进展，并总结开放问题以及该领域的未来方向。理论的进步将包括对普通，部分，延迟和分数微分方程系统的通用NSFD构造方法的潜在变革概念的探索。通过各种不同的微分方程模拟的经典或新兴兴趣的工程，科学和数学现象的各种工程，科学和数学现象的各种研究将得到强调。 Mickens教授的讲座将在专着中合并，将在其交叉路口统一这些不同的研究领域，并将作为推动数学科学以及其他科学和工程学科的理解，发现和跨学科合作的资源。更多会议信息将在http://www.ncat.edu/~math/cbms2020/this奖中获得，这反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评估审查标准来通过评估来获得支持的。